Aviezri Fraenkel's Home Page

Preprints, reprints, and access to the Games Bibliography and Responsa Project.

Aviezri Fraenkel's Home Page

This page lists some of my preprints, recent reprints, and indicates how to access my Games Bibliography. Also my special favorite, the Responsa Project,which is used worldwide, is mentioned briefly. It is a full text storage and retrieval system, preceeding Google by 35 years. In 2007 it was awarded the prestigious Israel Prize.

I. Some Preprints

II. English Reprints

III. Hebrew Transliterated Reprints

I. Some Preprints

  • A.S. Fraenkel, T. Gold, Sinai o oker harim, in Hebrew.
  • A.S.Fraenkel,Complementary balanced words over an arbitrary finite https://link.springer.com/content/pdf/10.1007/s42979-024-02679-7.pdf
  • A.S. Fraenkel, lzichro shel Tzvi Betzer za"l, in Hebrew.
  • A.S. Fraenkel, Tzadikim Urshaim b'mas' Horayot, in Hebrew. Preprint.
  • A.S. Fraenkel, Leket Al Birkat Hachamah, in Hebrew. Preprint.
  • A.S. Fraenkel, Hachodesh hazeh lachem roshhttps://link.springer.com/content/pdf/10.1007/s42979-024-02679-7.pdf . chodashim, in Hebrew. Preprint.
  • A.S. Fraenkel, Ichud olamot, in Hebrew. Preprint.
  • A.S. Fraenkel, Mah'peichat hamach'sheiv bcheikeir eitz haTorah, in Hebrew. Preprint.
  • A.S. Fraenkel, Tzvi Betzer Z"L -- gareis, dayeik v'yakir, in Hebrew. Preprint.

    • II. English Reprints

  • O. Amir, A.Amir, A.S Fraenkel, D. Sarne, On the Practical Power of Automata in Pattern Matching, Springer Nature Computer Science Journal, 6 April 2024.
  • A.S. Fraenkel, Solomon W. Golomb's Enlightening Games, in: The Wisdom of Solomon, The Genius and Legacy of Solomon Golomb, 165-168, 2023.
  • A.S Fraenkel, Patrolling the Border of a Striking Conjecture, , INTEGERS, Electr. J. Combinatorial Number Theory 22, 6pp, 2022
  • A.S. Fraenkel and U. Larsson, Games on arbitrarily large rats and playability, INTEGERS, Electr. J. Combinatorial Number Theory 19, 29pp, 2019.
  • E. Duchene, A.S. Fraenkel, V. Gurvich, N.B. Ho, C. Kimberling and U. Larsson, Wythoff Visions, In: Games of No Chance 5, Proc. BIRS Workshop on Combinatorial Games, 2008, Banff, Alberta, Canada, MSRI Publ. (U. Larsson, ed.), Vol. 70, Cambridge University Press, Cambridge, pp. 35--87, 2019.
  • A.S. Fraenkel and U. Larsson, Take-away games on Beatty's Theorem and the notion of k-invariance, In: Games of No Chance 5, Proc. BIRS Workshop on Combinatorial Games, 2008, Banff, Alberta, Canada, MSRI Publ. (U. Larsson, ed.), Vol. 70, Cambridge University Press, Cambridge, pp. 333--342, 2019.
  • A.S. Fraenkel, U. Larsson, C. P. Santos & B. von Stengel, Editorial, Special issue on combinatorial game theory, Intern. J. Game Theory, 47 no. 2 (2018) 375 - 377.
  • L. Goldberg and A.S. Fraenkel, Rulesets For Beatty Games, Intern. J. Game Theory, special issue on combinatorial games. 47 no. 2 (2018) 577 - 594.
  • L. Goldberg and A.S. Fraenkel, Patterns in the generalized Fibonacci word, applied to games, Discrete Math. 341 (2018) 1675-1687.
  • H. Li, S. Liu and A.S. Fraenkel, Extensions and restrictions of generakized Wythoff, 1--20.
    • H. Li, S. Liu, A.S. Fraenkel and W.A. Liu, Variants of $(s,t)$ Wythoff's games, Discrete Appl. Math. 227 (2017) 1-12.
  • G.E. Andrews, A.S. Fraenkel and J.A. Sellers, G.E. Andrews, A.S. Fraenkel and J.A. Sellers, $m$-ary partitions with no gaps: a characterization modulo $m$, Discrete Math. 339 (2016), pp. 283-287; DOI information:10.1016/j.disc.2015.08.016.
  • A.S. Fraenkel, M. Rigo, Games derived from a generalized Thue-Morse word, Intern. J. of Game Theory 1--13 (also in Combin. game theory colloq. Abstract), 2016
  • G.E. Andrews, A.S. Fraenkel and J.A. Sellers, Characterizing the number of $m$-ary partitions modulo $m$, Amer. Math. Monthly, 122 (2015), no. 9, 880-885, 2015. Copyright November 2015 Mathematical Association of America. All Rights Reserved.
  • A.S. Fraenkel and N.B. Ho, When are translati ons of P-positions of Wythoff's game P-positions?, INTEGERS 15A, #A4, 12 pp., Proc. INTEGERS 2013 Conference, The Erdos Centennial Conference, 2015.
  • F. Chung, C. Greene, J. Hutchinson -- Eds., Contributors; D.E. Knuth, A.S. Fraenkel, D. Zeilberger, M. Petkovsek, N. Calkin, R. Canfield, A. Nijenhuis, C.D. Savage, R.P. Stanley, F. Lazbenik -- Contributers, Herbert S. Wilf (1931-2012) Remembrance, Notices AMS. vol. 62, No. 4, 346--360, April 2015. Full article at: http://www.math.ucsd.edu/~fan/wilf/hw-ref.pdf .
  • A.S. Fraenkel and U. Peled, Harnessing the unwieldy MEX function, In: Games of No Chance 4, Proc. BIRS Workshop on Combinatorial Games, 2008, Banff, Alberta, Canada, MSRI Publ. (R.J. Nowakowski, ed.), Vol. 63, Cambridge University Press, Cambridge, pp. 77--94, 2015.
  • A.S. Fraenkel, The Rat game and the Mouse game, In: Games of No Chance 4, Proc. BIRS Workshop on Combinatorial Games, 2008, Banff, Alberta, Canada, MSRI Publ. (R.J. Nowakowski, ed.), Vol. 63, Cambridge University Press, Cambridge, pp. 95--113, 2015.
  • A.S. Fraenkel, R.A. Hearn and A.N. Siegel, Theory of combinatorial games, Chapter 15 in: Handbook of Game Theory, Volume 4 (H. Peyton Young and Shmuel Zamir, eds.), pp. 811- 859, Elsevier 2015.
  • A.S. Fraenkel, Integrating and Rejuvenating Old and New Gems, In Language, Culture, Computation, Essayss Dedicated to Yaacov Choueka on the Occasion of His 75th Birthday, Part I, pp. 37--49, Springer, 2014.
  • A. Fink, A.S. Fraenkel and C. Santos, Lim Is not Slim, Internat. J. Game Theory (2014) 43:269-281 DOI 10.1007/s00182-013-0380-z http://link.springer.com/article/10.1007%2Fs00182-013-0380-z#page-1.
  • A.S. Fraenkel, Beating Your Fractional Beatty Game Opponent and: What's the Question to Your Answer? , in: Advances in Combinatorics, in Memory of Herbert S. Wilf, Proc. Waterloo Workshop on Computer Algebra, I.S. Kotsireas and E.V. Zima, eds., May 2011, pp. 175-186, Springer 2013.
  • A.S. Fraenkel and Y. Tanny, A Class of Wythoff-Like Games , Proc. INTEGERS Conference, Carrollton, Georgia, Oct. 26-29, 2011, in: INTEGERS, Electr. J. Combinat. Number Theory 12(B) (2013) #A7, 18pp. Also in Combinatorial Number Theory, pp. 91-107, de Gruyter 2013. [Archive of INTEGERS.]
  • A.S. Fraenkel, Ratwyt, In memory of Martin Gardner, The College Math. J., March 2012, pp. 160-164.
  • A.S. Fraenkel, The vile, dopey, evil and odious game players, Discrete Math. 312 (2012) 42-46, special volume in honor of the 80th birthday of Gert Sabidussi.
  • A.S. Fraenkel, Aperiodic subtraction games, Electronic J. Combinatorics vol. 18(2) P19 12pp., 2011. http://www.combinatorics.org/Journal/journalhome.html
  • S. Blanco and A.S. Fraenkel, Tromping Games: Tiling with Trominoes, Proc. INTEGERS Conference, in honor of the birthdays of Melvyn Nathanson and Carl Pomerance, Carrollton, Georgia, Oct. 14-17, 2009, in: INTEGERS, Electr. J. Combinat. Number Theory 11(A) (2011) #6, 29pp.
  • U. Larsson, P. Hegarty and A.S. Fraenkel, Invariant and dual subtraction games resolving the Duchene-Rigo conjecture, Theoretical Computer Science 412 (2011), 729-735.
  • A.S. Fraenkel, From enmity to amity. Amer. Math. Monthly 117 (2010), 646--648.
  • A.S. Fraenkel, Complementary Iterated Floor Words and the Flora Game. SIAM J. on Discrete Math 24 (2010), 570--588.
  • E. Duchene, A.S. Fraenkel, R.J. Nowakowski and M. Rigo, Extensions and restrictions of Wythoff's game preserving its P-positions. J. Combinat. Theory A 117 (2010), 545--567.
  • J. Bell, E. Charlier, A.S. Fraenkel, M. Rigo, A decision problem for ultimately periodic sets in non-standard numeration systems. Internat. J. Algebra Computat 19 (2009), 6, 809--839.
  • A.S. Fraenkel and E. Reisner, The game of End-Wythoff, in Games of No Chance 3, Proc. BIRS Workshop on Combinatorial Games, July 2005, Banff, Alberta, Canada, MSRI Publ. (M.H. Albert and R.J. Nowakowski, eds.), Vol. 56, Cambridge University Press, Cambridge, pp. 329-347, 2009.
  • A.S. Fraenkel, The cyclic Butler University game, in: Mathematical Wizardry for a Gardner (E. Pegg Jr, A.H. Schoen, and T. Rodgers, eds.), in honor of Martin Gardner, pp. 97-105, A K Peters, Natick, MA, 2009.
  • E. Duchene, A.S. Fraenkel, S. Gravier and R.J. Nowakowski, Another bridge between Nim and Wythoff, Australasian J. of Combinatorics 44 (2009), 43--56.
  • S. Artstein-Avidan, A.S. Fraenkel and V. Sos, A two-parameter family of an extension of Beatty sequences, Discrete Math 308 (2008) 4578-4588.
  • A.S. Fraenkel, Games played by Boole and Galois, Discrete Appl. Math., 156 (2008) 420-427.
  • P.J. Davis and A.S. Fraenkel, Remembering Philip Rabinowitz, Notices AMS 54 (2007) 1502-1506. Reprinted, with the permission of the AMS, in The Birth of Numerical Analysis (A. Bultheel, R. Cools, eds.) World Scientific (2009) 179-185.
  • A.S. Fraenkel, The Raleigh game. in: Combinatorial Number Theory, Proc. INTEGERS Conference 2005, in celebration of the 70th birthday of Ronald Graham, Carrollton, Georgia, Oct. 27-30, 2005; B. Landman, M. Nathanson, J. Nesetril, R. Nowakowski, C. Pomerance, eds., de Gruyter, pp. 199-208, 2007. Also appeared in INTEGERS, Electr. J. Combinat. Number Theory 7(2) (2007) #13, 11pp., special volume in honor of Ron Graham.
  • A.S. Fraenkel and A. Kontorovich, The Sierpinski sieve of Nim-varieties and binomial coefficients. in: Combinatorial Number Theory, Proc. Integers Conference 2005, in celebration of the 70th birthday of Ronald Graham, Carrollton, Georgia, Oct. 27-30, 2005; B. Landman, M. Nathanson, J. Nesetril, R. Nowakowski, C. Pomerance, eds., de Gruyter, pp. 209-227, 2007. Also appeared in INTEGERS, Electr. J. Combinat. Number Theory 7(2) (2007) #14, 19pp., special volume in honor of Ron Graham.
  • A.S. Fraenkel, Why are games exciting and stimulating?, Math Horizons February 2007, 5--7; 32--33. A German translation, by Niek Neuwahl, was poster-displayed at the ``Games & Science, Science & Games" exhibition, which took place in Goettingen, July 17 -- Aug 21, 2005. It was selected as runner up for an EMS Article Competition 2005 for the educated layman.
  • A.S. Fraenkel, Nim is easy, chess is hard --- but why??, J. Internat. Computer Games Assoc. 29 (2006) 203--2006. Earlier shorter version appeared in Plus Mag. (electronic) issue 40, pluschat section, Sept., 2006.
  • A.S. Fraenkel, Euclid and Wythoff games, Discrete Math. 304 (2005) 65--68.
  • Aviezri S. Fraenkel and Jamie Simpson, An extension of the periodicity lemma to longer periods, Discrete Appl. Math. 146 (2005) 146-155 (special issue of 12th Annual Symposium on Combinatorial Pattern Matching). Preliminary version appeared in Proc. 12th Annual Sympos. Combinatorial Pattern Matching, Jerusalem, Israel, July 1--4, 2001 (A. Amir and G. M. Landau, eds.), Lecture Notes in Computer Science, Springer, Berlin, pp. 98--105) (invited).
  • A.S. Fraenkel, New games related to old and new sequences. INTEGERS, Electronic J. Combinat. Number Theory 4 (2004) #G06, 18pp. http://www.integers-ejcnt.org . First version appeared in Advances in Computer Games, Proc. 10-th Advances in Computer Games Conference (ACG-10), Nov. 2003, Graz, Austria (H.J. van den Herik, H. Iida, E.A. Heinz, eds.), pp. 367--382, Kluwer.
  • A.S. Fraenkel, Complexity, appeal and challenges of combinatorial games, Expanded version of a keynote address at Dagstuhl Seminar Feb.~17--22, 2002, Theoretical Computer Science 313 (2004) 393-415, special issue on Algorithmic Combinatorial Game Theory.
  • S.P. Fekete, R. Fleischer, A.S. Fraenkel and M. Schmitt, Traveling salesmen in the presence of competition, Theoretical Computer Science 313 (2004) 377-392, special issue on Algorithmic Combinatorial Game Theory.
  • E.D. Demaine, R. Fleischer, A.S. Fraenkel and R.J. Nowakowski, Open problems at the 2002 Dagstuhl Seminar on Algorithmic combinatorial game theory, Theoretical Computer Science 313 (2004) 539-543, special issue on Algorithmic Combinatorial Game Theory (Appendix B).
  • A.S. Fraenkel and Dalia Krieger, The structure of complementary sets of integers: a 3-shift theorem, Internat. J. Pure and Appl. Math. 10 (2004) 1--49.
  • Aviezri S. Fraenkel and Ofer Rahat, Complexity of error-correcting codes derived from combinatorial games, Proc. Intern. Conference on Computers and Games CG'2002, Edmonton, Alberta, Canada, July 2002 (Y. Bj\"{o}rnsson, M.\ M\"{u}ller, J. Schaeffer, eds.), Lecture Notes in Computer Science LNCS 2883, pp. 201--212, Springer 2003.
  • Aviezri S. Fraenkel, Jamie Simpson and Mike Paterson, On abelian circular squares in binary words. In: Paul Erdos and his Mathematics II, Bolyai Soc., Mathematical Studies 11, Budapest 2002, pp. 329--338. An earlier version entitled ``On weak circular squares in binary words'' appeared in Proc. 8th Annual Symposium on Combinatorial Pattern Matching, Aarhus, Denmark, June 30--July 2, 1997 (A. Apostolico and J. Hein, eds.), Lecture Notes in Computer Science, Springer, Berlin, pp. 76--82).
  • A.S. Fraenkel, Two-player games on cellular automata, in More Games of No Chance, Proc. MSRI Workshop on Combinatorial Games, July 10--28, 2000, Berkeley, CA (R. J. Nowakowski, ed.), Cambridge University Press, Cambridge, Vol. 42, 2002, pp. 279--306.
  • A.S. Fraenkel, Arrays, numeration systems and Frankenstein games, Theoretical Computer Science 282 (2002) 271--284 (special "FUN in Algorithms" issue).
  • A.S. Fraenkel, Mathematical Chats Between Two Physicists, in Puzzlers' Tribute: A Feast for the Mind, honoring Martin Gardner (D. Wolfe and T. Rodgers, eds.), A K Peters, 2002, pp. 315--325.
  • A.S. Fraenkel, Virus versus mankind, in: Proc. 2nd Intern. Conference on Computer Games CG'2000, Hamamatsu, Japan, Oct. 2000, Lecture Notes in Computer Science, Springer (T. Marsland, I. Frank, eds.), 2001, pp. 204--213.
  • A.S. Fraenkel, T. Seeman and J. Simpson The subword complexity of a two-parameter family of sequences, Electronic J. Combinatorics vol. 8(2) R10, 2001 http://www.combinatorics.org/Journal/journalhome.html
  • A.S. Fraenkel, A Selection Of Mathematical Board Games, Abstract Presented at Board Games in Academia III, Florence, April 12--15, 1999. Proceedings Board Games in Academia III, pp. 46--67.
  • A.S. Fraenkel and D. Zusman, A New Heap Game, Theoretical Computer Science 252 (2001) 5--12 (special "Computers and Games issue"). Initial version appeared in Lecture Notes in Computer Science 1558, Proc. 1-st Intern. Conference on Computer Games, Tsukuba, Japan, Nov. 1998, pp. 205--211, 1999.
  • A.S. Fraenkel and O. Rahat, Infinite cyclic impartial games, Theoretical Computer Science 252 (2001) 13-22 (special "Computers and Games issue"). Initial version appeared in Lecture Notes in Computer Science 1558, Proc. 1-st Intern. Conference on Computer Games, Tsukuba, Japan, Nov. 1998, pp. 212--221, 1999.
  • A.S. Fraenkel, Recent results and questions in combinatorial game complexities, Expanded version of invited lecture at Ninth Australasian Workshop on Combinatorial Algorithms, Perth, Western Australia, 27---30 July 1998, Theoret. Comput. Sci. 249 (2000) 265--288. Conference version in: Proc. AWOCA98 --- Ninth Australasian Workshop on Combinatorial Algorithms, (C.S. Iliopoulos, ed.), pp. 124--146.
  • A.S. Fraenkel, On the recurrence f(m+1)=b(m)f(m)-f(m-1) and applications, Discrete Mathematics 224 (2000) 273--279 (Note).
  • A.S. Fraenkel and S.T. Klein, Information retrieval from annotated texts, J. Amer. Soc. for Information Sciences 50 (1999) 845--854.
  • A.S. Fraenkel and Jamie Simpson, The exact number of squares in Fibonacci words, Theoret. Comput. Sci. 218 (1999) 95--106 (special Words issue).
  • A.S. Fraenkel, Protein folding, spin glass and computational complexity, Expanded form of invited paper presented at DNA Based Computers III, Proc. DIMACS Workshop (H. Rubin and D. H. Wood, Eds.), June 23--25, 1997, University of Pennsylvania, DIMACS Series in Discrete Mathematics and Theoretical Computer Science Vol. 48, AMS, 1999, pp. 101--121.
  • A.S. Fraenkel, Heap games, numeration systems and sequences, Annals of Combinatorics 2 (1998) 197--210.
  • U.Blass, A.S. Fraenkel and R. Guelman, How far can Nim in disguise be stretched?, J. Combin. Theory (Ser. A) 84 (1998) 145--156.
  • A.S. Fraenkel, The Responsa storage and retrieval system---whither? The Hebrew version: Proyect hashut: avar, hoveh---v'gam atid? appeared in Dinei Yisrael 19 (1997-98) 253--270.
  • A.S. Fraenkel and Michal Ozery, Adjoining to Wythoff's game its P-positions as moves, Theoretical Computer Science 205 (1998) 283--296.
  • A.S. Fraenkel, Multivision: a game of arbitrarily long play, Amer. Math. Monthly 105 (1998) 923--928.
  • A.S. Fraenkel and Jamie Simpson, How many squares can a string contain? J. Combin. Theory Ser. A 82 (1998) 112--120. Errata: In Table 1, the number of maximal words (last column) should be 6 and 72 for n=3 and n=12 respectively. These corrections do not otherwise affect the results of the paper. We thank Troy Vasiga for pointing out the first of these typos.
  • A.S. Fraenkel, Systems of numeration, AMM 1985, 105--114.
  • A.S. Fraenkel and D. Lichtenstein, Computing a perfect strategy for n x n chess requires time exponential in n, J. Combin. Theory Ser. A 31 (1981) 1 99--214.
  • M. Boshernitzan and A.S. Fraenkel, Nonhomogenious spectra of numbers, Discrete Math., Communication (1981) 325--327
  • A.S. Fraenkel, Combinatorial game theory foundations applied to digraph kernels , Electronic J. of Combinatorics 4(2) (1997) R10, 17pp. (Wilf Festschrift).
  • A.S. Fraenkel, and S.Simonson, Geography. Theoretical Comput. Sci.110(1993),no. 1, 197–214. M.A. Berger, A. Felzenbaum, A.S.Fraenkel and R.Holzman,On infinite and finite covering systems.Amer. Math. Monthly98(1991),no. 8,739–742. M.A. Berger, A. Felzenbaum asnd Fraenkel, Aviezri S.Irreducible disjoint covering systems (with an application to Boolean algebra).First International Colloquium on Pseudo-Boolean Optimization and Related Topics (Chexbres, 1987).Discrete Appl. Math.29(1990),no. 2-3,143–164.
    MR4363103ReviewedFraenkel, Aviezri S.Patrolling the border of a striking conjecture.Integers22(2022),Paper No. A3, 6 pp.11B75
    Review PDFClipboardArticle
    MR4188748ReviewedFraenkel, Aviezri S.;Larsson, UrbanGames on arbitrarily large rats and playability.Integers19(2019),Paper No. G04, 29 pp. (Reviewer: Grant Cairns)91A46 (05A17 11B75)
    Review PDFClipboardArticle3 Citations
    MR3965376ReviewedFraenkel, Aviezri S.;Larsson, UrbanTake-away games on Beatty's theorem and the notion ofk-invariance.Games of no chance 5,333–342,Math. Sci. Res. Inst. Publ., 70,Cambridge Univ. Press, Cambridge,2019.91A46
    Review PDFClipboardChapter1 Citation
    MR3965364ReviewedDuchne, Eric;Fraenkel, Aviezri S.;Gurvich, Vladimir;Ho, Nhan Bao;Kimberling, Clark;Larsson, UrbanWythoff visions.Games of no chance 5,35–87,Math. Sci. Res. Inst. Publ., 70,Cambridge Univ. Press, Cambridge,2019.91A46 (91-02)
    Review PDFClipboardChapter5 Citations
    MR3842044ReviewedGoldberg, Lior;Fraenkel, Aviezri S.Rulesets for Beatty games.Internat. J. Game Theory47(2018),no. 2,577–594.91A46
    Review PDFClipboard1 Citation
    MR3842035IndexedFraenkel, Aviezri;Larsson, Urban;Santos, Carlos P.;von Stengel, BernhardSpecial issue on combinatorial game theory.Internat. J. Game Theory47(2018),no. 2,375–377.91-06 (91A46)
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    MR3784788ReviewedGoldberg, Lior;Fraenkel, Aviezri S.Patterns in the generalized Fibonacci word, applied to games.Discrete Math.341(2018),no. 6,1675–1687.68R15 (91A46)
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    MR3661410ReviewedLi, Haiyan;Liu, Sanyang;Fraenkel, Aviezri S.;Liu, Wen AnVariants of(s,t)-Wythoff's game.Discrete Appl. Math.227(2017),1–12. (Reviewer: Grant Cairns)91A46
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    MR3404489ReviewedAndrews, George E.;Fraenkel, Aviezri S.;Sellers, James A.m-ary partitions with no gaps: a characterization modulom.Discrete Math.339(2016),no. 1,283–287.05A17 (05A15 11P81)
    Review PDFClipboard5 Citations
    MR3560331ReviewedFraenkel, Aviezri S.The Rat game and the Mouse game.Games of no chance 4,95–113,Math. Sci. Res. Inst. Publ., 63,Cambridge Univ. Press, New York,2015.91A46
    Review PDFClipboardChapter8 Citations
    MR3560330ReviewedFraenkel, Aviezri S.;Peled, UdiHarnessing the unwieldy MEX function.Games of no chance 4,77–94,Math. Sci. Res. Inst. Publ., 63,Cambridge Univ. Press, New York,2015. (Reviewer: Grant Cairns)91A46
    Review PDFClipboardChapter10 Citations
    MR3418210ReviewedAndrews, George E.;Fraenkel, Aviezri S.;Sellers, James A.Characterizing the number ofm-ary partitions modulom.Amer. Math. Monthly122(2015),no. 9,880–885. (Reviewer: David M. Bressoud)05A17 (11P83)
    Review PDFClipboard9 Citations
    MR3361813ReviewedFraenkel, Aviezri S.;Ho, Nhan BaoWhen are translations ofP-positions of Wythoff's gameP-positions?Integers15A(2015),Paper No. A4, 12 pp. (Reviewer: Paweł Prałat)91A46 (91A05)
    Review PDFClipboardArticle3 Citations
    MR3233468IndexedFraenkel, Aviezri S.;Simpson, JamieCorrigendum to "The exact number of squares in Fibonacci words'' [Theoret. Comput. Sci. 218 (1) (1999) 95–106] [MR1687768].Theoret. Comput. Sci.547(2014),122.68R15 (11B39)
    Review PDFClipboardJournal1 Citation
    MR3197293ReviewedFink, Alex;Fraenkel, Aviezri S.;Santos, CarlosLIM is not slim.Internat. J. Game Theory43(2014),no. 2,269–281. (Reviewer: Nhan Bao Ho)91A46 (68Q80)
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    MR3363969ReviewedFraenkel, Aviezri S.Beating your fractional Beatty game opponent and: what's the question to your answer?Advances in combinatorics,175–186,Springer, Heidelberg,2013. (Reviewer: Nhan Bao Ho)91A46
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    MR3220917IndexedFraenkel, Aviezri S.;Tanny, YuvalA class of Whythoff-like games [reprint ofMR3055681].Combinatorial number theory,91–107,De Gruyter Proc. Math.,De Gruyter, Berlin,2013.91A46
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    MR3055681ReviewedFraenkel, Aviezri;Tanny, YuvalA class of Wythoff-like games.Integers12B(2012/13),Proceedings of the Integers Conference 2011,Paper No. A7, 18 pp. (Reviewer: Nhan Bao Ho)91A46
    Review PDFClipboardArticle6 Citations
    MR2897480ReviewedFraenkel, Aviezri S.RATWYT.College Math. J.43(2012),no. 2,160–164.91A46 (11B75 91A26)
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    MR2852506IndexedFraenkel, Aviezri S.The vile, dopey, evil and odious game players.Discrete Math.312(2012),no. 1,42–46.91A46
    Review PDFClipboard7 Citations
    MR2988066ReviewedBlanco, Sal A.;Fraenkel, Aviezri S.Tromping games: tiling with trominoes.Integers11(2011),no. 3,333–362. (Reviewer: Grant Cairns)91A46 (05B50)
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    MR2830984ReviewedFraenkel, Aviezri S.Aperiodic subtraction games.Electron. J. Combin.18(2011),no. 2,Paper 19, 12 pp. (Reviewer: Peter Vincent Hegarty)91A46 (11B75 68Q25 91A05)
    Review PDFClipboardArticle11 Citations
    MR2796920ReviewedLarsson, Urban;Hegarty, Peter;Fraenkel, Aviezri S.Invariant and dual subtraction games resolving the Duchne-Rigo conjecture.Theoret. Comput. Sci.412(2011),no. 8-10,729–735. (Reviewer: Andrs Sndor Pluhr)91A46
    Review PDFClipboard9 Citations
    MR2681526IndexedFraenkel, Aviezri S.From enmity to amity.Amer. Math. Monthly117(2010),no. 7,646–648.11B83
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    MR2661423ReviewedFraenkel, Aviezri S.Complementary iterated floor words and the Flora game.SIAM J. Discrete Math.24(2010),no. 2,570–588. (Reviewer: E. J. Barbeau)91A46 (05A05 11B75)
    Review PDFClipboard5 Citations
    MR2604147IndexedDavis, Philip J.;Fraenkel, Aviezri S.Remembering Philip Rabinowitz [reprint ofMR2361163].The birth of numerical analysis,179–186,World Sci. Publ., Hackensack, NJ,2010.65-03 (01A70 65D30)
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    MR2600974ReviewedDuchne, Eric;Fraenkel, Aviezri S.;Nowakowski, Richard J.;Rigo, MichelExtensions and restrictions of Wythoff's game preserving itsPpositions.J. Combin. Theory Ser. A117(2010),no. 5,545–567. (Reviewer: Thane Earl Plambeck)91A46 (91A43)
    Review PDFClipboard33 Citations
    MR2572876ReviewedBell, Jason;Charlier, Emilie;Fraenkel, Aviezri S.;Rigo, MichelA decision problem for ultimately periodic sets in nonstandard numeration systems.Internat. J. Algebra Comput.19(2009),no. 6,809–839. (Reviewer: Petr Ambrož)68Q45 (03B25 11B85 11U05)
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    MR2526997ReviewedDuchne, E.;Fraenkel, A. S.;Gravier, S.;Nowakowski, R. J.Another bridge between NIM and WYTHOFF.Australas. J. Combin.44(2009),43–56. (Reviewer: Thane Earl Plambeck)91A46
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    MR2438162ReviewedArtstein-Avidan, Shiri;Fraenkel, Aviezri S.;Ss, Vera T.A two-parameter family of an extension of Beatty sequences.Discrete Math.308(2008),no. 20,4578–4588.05B45 (91A46)
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    MR2379074ReviewedFraenkel, Aviezri S.Games played by Boole and Galois.Discrete Appl. Math.156(2008),no. 4,420–427.91A46
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    MR2361163IndexedDavis, Philip J.;Fraenkel, Aviezri S.Remembering Philip Rabinowitz.Notices Amer. Math. Soc.54(2007),no. 11,1502–1506.01A70
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    MR2337048ReviewedFraenkel, Aviezri S.;Kontorovich, AlexThe Sierpiński sieve of Nim-varieties and binomial coefficients.Combinatorial number theory,209–227,de Gruyter, Berlin,2007. (Reviewer: Kimmo Eriksson)05A10 (11B65 91A46)
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    MR2337047ReviewedFraenkel, Aviezri S.The Raleigh game.Combinatorial number theory,199–208,de Gruyter, Berlin,2007. (Reviewer: E. J. Barbeau)91A46 (91A05)
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    MR2184445ReviewedFraenkel, Aviezri S.Euclid and Wythoff games.Discrete Math.304(2005),no. 1-3,65–68.91A05 (91A46)
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    MR2111926ReviewedFraenkel, Aviezri S.;Simpson, JamieAn extension of the periodicity lemma to longer periods.Discrete Appl. Math.146(2005),no. 2,146–155.68R15 (05A05)
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    MR2116012ReviewedFraenkel, Aviezri S.New games related to old and new sequences.Integers4(2004),G6, 18 pp. (Reviewer: David Damanik)11B83 (91A05)
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    MR2056945IndexedDemaine, Erik D.;Fleischer, Rudolf;Fraenkel, Aviezri;Nowakowski, Richard J.Appendix B: Open problems at the 2002 Dagstuhl Seminar on Algorithmic Combinatorial Game Theory.Algorithmic combinatorial game theory.Theoret. Comput. Sci.313(2004),no. 3,539–543.91A46
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    MR2056935IndexedFraenkel, Aviezri S.Complexity, appeal and challenges of combinatorial games.Algorithmic combinatorial game theory.Theoret. Comput. Sci.313(2004),no. 3,393–415.91A46 (05A99 68Q25)
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    MR2056934ReviewedFekete, Sndor P.;Fleischer, Rudolf;Fraenkel, Aviezri;Schmitt, MatthiasTraveling salesmen in the presence of competition.Algorithmic combinatorial game theory.Theoret. Comput. Sci.313(2004),no. 3,377–392.90C35 (68Q17 91A05)
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    MR2042724IndexedFraenkel, A. S.New games related to old and new sequences.Advances in computer games (Graz, 2003),367–382,IFIP Int. Fed. Inf. Process., 135,Kluwer Acad. Publ., Boston, MA,2004.91A46
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    MR2020683ReviewedFraenkel, Aviezri S.;Krieger, DaliaThe structure of complementary sets of integers: a 3-shift theorem.Int. J. Pure Appl. Math.10(2004),no. 1,1–49. (Reviewer: A. Ya. Olenko)05A17 (05A05 91A05)
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    MR1973111IndexedFraenkel, Aviezri S.Combinatorial games: selected bibliography with a succinct gourmet introduction.More games of no chance (Berkeley, CA, 2000),475–535,Math. Sci. Res. Inst. Publ., 42,Cambridge Univ. Press, Cambridge,2002.91A46
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    MR1973018ReviewedFraenkel, Aviezri S.Two-player games on cellular automata.More games of no chance (Berkeley, CA, 2000),279–306,Math. Sci. Res. Inst. Publ., 42,Cambridge Univ. Press, Cambridge,2002.91A05 (05C85 68Q80 91A43 91A46)
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    MR1954732ReviewedFraenkel, A. S.;Simpson, R. J.;Paterson, M. S.On abelian circular squares in binary words.Paul Erdős and his mathematics, II (Budapest, 1999),329–338,Bolyai Soc. Math. Stud., 11,Jnos Bolyai Math. Soc., Budapest,2002.68R15 (05A05)
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    MR1909611IndexedFraenkel, Aviezri S.Virus versus mankind.Computers and games (Hamamatsu, 2000),204–213,Lecture Notes in Comput. Sci., 2063,Springer, Berlin,2002.05C99 (68Q80 91A43)
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    MR1909052ReviewedFraenkel, Aviezri S.Arrays, numeration systems and Frankenstein games.FUN with algorithms (Elba, 1998).Theoret. Comput. Sci.282(2002),no. 2,271–284. (Reviewer: Prabir Das)91A46 (11B37)
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    MR1904570IndexedFraenkel, Aviezri S.;Simpson, JamieAn extension of the periodicity lemma to longer periods (invited lecture).Combinatorial pattern matching (Jerusalem, 2001),98–105,Lecture Notes in Comput. Sci., 2089,Springer, Berlin,2001.68R15
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    MR1853261ReviewedFraenkel, Aviezri S.;Seeman, Tamar;Simpson, JamieThe subword complexity of a two-parameter family of sequences.In honor of Aviezri Fraenkel on the occasion of his 70th birthday.Electron. J. Combin.8(2001),no. 2,Research Paper 10, 19 pp. (Reviewer: Walter Kern)91A05 (68R15)
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    MR1806223ReviewedFraenkel, Aviezri S.;Rahat, OferInfinite cyclic impartial games.Computer and games (Tsukuba, 1998).Theoret. Comput. Sci.252(2001),no. 1-2,13–22.91A43 (05C20)
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    MR1806222ReviewedFraenkel, Aviezri S.;Zusman, DmitriA new heap game.Computer and games (Tsukuba, 1998).Theoret. Comput. Sci.252(2001),no. 1-2,5–12.91A46 (68T20)
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    MR1798313ReviewedFraenkel, Aviezri S.Recent results and questions in combinatorial game complexities.Combinatorial algorithms (Perth, 1998).Theoret. Comput. Sci.249(2000),no. 2,265–288. (Reviewer: Daniel Elliott Loeb)91A46 (68Q25 68R05 91A40)
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    MR1781301ReviewedFraenkel, Aviezri S.On the recurrencefm+1=bmfm−fm−1and applications.Discrete Math.224(2000),no. 1-3,273–279. (Reviewer: Vichian Laohakosol)39A10 (11A55 40A15)
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    MR1715689ReviewedFraenkel, Aviezri S.;Rahat, OferInfinite cyclic impartial games.Computers and games (Tsukuba, 1998),212–221,Lecture Notes in Comput. Sci., 1558,Springer, Berlin,1999. (Reviewer: P. A. Biryukov)91A46 (05C20)
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    MR1715688ReviewedFraenkel, Aviezri S.;Zusman, DmitriA new heap game.Computers and games (Tsukuba, 1998),205–211,Lecture Notes in Comput. Sci., 1558,Springer, Berlin,1999. (Reviewer: P. A. Biryukov)91A46
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    MR1688708ReviewedFraenkel, Aviezri S.Protein folding, spin glass and computational complexity.DNA based computers III (Philadelphia, PA, 1997),101–121,DIMACS Ser. Discrete Math. Theoret. Comput. Sci., 48,Amer. Math. Soc., Providence, RI,1999. (Reviewer: Stephen J. Willson)92D20 (68Q25 92-08)
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    MR1687768ReviewedFraenkel, Aviezri S.;Simpson, JamieThe exact number of squares in Fibonacci words.WORDS (Rouen, 1997).Theoret. Comput. Sci.218(1999),no. 1,95–106. (Reviewer: Patrice Sbold)68R15 (11B39)
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    MR1543394DMLFraenkel, Aviezri; Martin, Reiner;Problems and Solutions: Solutions: Sets with Fixed Nim-Sum: 10564.Amer. Math. Monthly106(1999),no. 1,71–72.
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    MR1681514ReviewedFraenkel, Aviezri S.Heap games, numeration systems and sequences.Ann. Comb.2(1998),no. 3,197–210.91A05 (05A99 91A46)
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    MR1656919ReviewedFraenkel, Aviezri S.Multivision: an intractable impartial game with a linear winning strategy.Amer. Math. Monthly105(1998),no. 10,923–928. (Reviewer: E. Marchi)90D46 (05A99)
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    MR1652900ReviewedBlass, Uri;Fraenkel, Aviezri S.;Guelman, RominaHow far can nim in diguise be stretched?J. Combin. Theory Ser. A84(1998),no. 2,145–156. (Reviewer: P. A. Biryukov)91A46 (05A99)
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    MR1638601ReviewedFraenkel, Aviezri S.;Ozery, MichalAdjoining to Wythoff's game itsP-positions as moves.Theoret. Comput. Sci.205(1998),no. 1-2,283–296. (Reviewer: P. A. Biryukov)90D46
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    MR1616571ReviewedFraenkel, Aviezri S.;Simpson, JamieHow many squares can a string contain?J. Combin. Theory Ser. A82(1998),no. 1,112–120.68R15 (11B85)
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    MR1608392ReviewedFraenkel, Aviezri S.;Simpson, Jamie;Paterson, MikeOn weak circular squares in binary words.Combinatorial pattern matching (Aarhus, 1997),76–82,Lecture Notes in Comput. Sci., 1264,Springer, Berlin,1997.68R15
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    MR1542936DMLFraenkel, Aviezri; Bloom, D. M.; Suman, Kenneth; Myerson, Gerry; Girod, Donald; Knuth, Donald E.; Priestley, W. M.; Deutsch, Emeric;Problems and Solutions: Problems: 10564-10570.Amer. Math. Monthly104(1997),no. 1,68–69.
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    MR1444157ReviewedFraenkel, Aviezri S.Combinatorial game theory foundations applied to digraph kernels.The Wilf Festschrift (Philadelphia, PA, 1996).Electron. J. Combin.4(1997),no. 2,Research Paper 10, approx. 17 pp.05C90 (05C85 68Q25 90D43)
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    MR1427984IndexedFraenkel, Aviezri S.Combinatorial games: selected bibliography with a succinct gourmet introduction.Games of no chance (Berkeley, CA, 1994),493–537,Math. Sci. Res. Inst. Publ., 29,Cambridge Univ. Press, Cambridge,1996.90D46 (90-00)
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    MR1427980ReviewedFraenkel, Aviezri S.Error-correcting codes derived from combinatorial games.Games of no chance (Berkeley, CA, 1994),417–431,Math. Sci. Res. Inst. Publ., 29,Cambridge Univ. Press, Cambridge,1996. (Reviewer: Ram Autar)94B05 (90D46)
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    MR1427955ReviewedFraenkel, Aviezri S.Scenic trails ascending from sea-level Nim to alpine chess.Games of no chance (Berkeley, CA, 1994),13–42,Math. Sci. Res. Inst. Publ., 29,Cambridge Univ. Press, Cambridge,1996. (Reviewer: Imma J. Curiel)90D46 (05C99 90D05)
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    MR1364104ReviewedJones, J. P.;Fraenkel, A. S.Complexities of winning strategies in Diophantine games.J. Complexity11(1995),no. 4,435–455. (Reviewer: John Michael Robson)68Q25 (03D15 68Q15 90D46)
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    MR1336680ReviewedFraenkel, Aviezri S.;Loebl, MartinComplexity of circuit intersection in graphs.Discrete Math.141(1995),no. 1-3,135–151. (Reviewer: Patrick Sol)05C85 (57M25)
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    MR1335685ReviewedFraenkel, Aviezri S.;Jaffray, Alan;Kotzig, Anton;Sabidussi, GertModular Nim.Theoret. Comput. Sci.143(1995),no. 2,319–333. (Reviewer: Edward W. Packel)90D05 (00A08 05A99 90D42)
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    MR1310736ReviewedFraenkel, Aviezri S.;Holzman, RonGap problems for integer part and fractional part sequences.J. Number Theory50(1995),no. 1,66–86. (Reviewer: Robert F. Tichy)11J71 (11K31)
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    MR1309124ReviewedFraenkel, Aviezri S.;Simpson, R. JamieHow many squares must a binary sequence contain?Electron. J. Combin.2(1995),Research Paper 2, approx. 9 pp. (Reviewer: kos Pintr)11B83 (05A99)
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    MR1670621IndexedFraenkel, Aviezri S.Combinatorial games: selected bibliography with a succinct gourmet introduction.Electron. J. Combin.1(1994),Dynamic Survey 2, 45 pp.90-00 (05A99 90Dxx)
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    MR1310872ReviewedFraenkel, A. S.;Porta, H.;Stolarsky, K. B.The almost PV behavior of some far from PV algebraic integers.Discrete Math.135(1994),no. 1-3,93–101. (Reviewer: D. Boyd)11R06 (11B37 11J71)
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    MR1289489ReviewedFraenkel, A. S.;Klein, S. T.Complexity aspects of guessing prefix codes.Algorithmica12(1994),no. 4-5,409–419. (Reviewer: Andrea Sgarro)94A60 (68P25 68Q15 94A29 94A45)
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    MR1274978ReviewedBronstein, Victor;Fraenkel, Aviezri S.On a curious property of counting sequences.Amer. Math. Monthly101(1994),no. 6,560–563. (Reviewer: Giuseppe Pellegrino)05A16
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    MR1269166ReviewedFraenkel, AviezriEven kernels.Electron. J. Combin.1(1994),Research Paper 5, approx. 13 pp. (Reviewer: Hans L. Bodlaender)05C70 (68Q25 68R10)
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    MR1264482ReviewedFraenkel, A. S.;Kimberling, ClarkGeneralized Wythoff arrays, shuffles and interspersions.Discrete Math.126(1994),no. 1-3,137–149. (Reviewer: Volker Strehl)11B83 (05A99)
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    MR1138949ReviewedFraenkel, Aviezri S.Iterated floor function, algebraic numbers, discrete chaos, Beatty subsequences, semigroups.Trans. Amer. Math. Soc.341(1994),no. 2,639–664. (Reviewer: Štefan Porubsk)11B83 (11B39 11Z50 58F13)
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    MR1216328ReviewedFraenkel, Aviezri S.;Scheinerman, Edward R.;Ullman, DanielUndirected edge geography.Theoret. Comput. Sci.112(1993),no. 2,371–381.90D35 (68Q25)
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    MR1210094ReviewedEggleton, Roger B.;Fraenkel, Aviezri S.;Simpson, R. JamieBeatty sequences and Langford sequences.Graph theory and combinatorics (Marseille-Luminy, 1990).Discrete Math.111(1993),no. 1-3,165–178. (Reviewer: Š. Znm)11B25 (05A10)
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    MR1208665ReviewedFraenkel, A. S.;Simonson, S.Geography.Theoret. Comput. Sci.110(1993),no. 1,197–214.90D40 (05C85 68Q25 68R10 90D35)
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    MR1148023ReviewedFraenkel, Aviezri S.;Simpson, R. JamieOn infinite disjoint covering systems.Proc. Amer. Math. Soc.119(1993),no. 1,5–9. (Reviewer: Š. Znm)11B25
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    MR1214102ReviewedBarabash, Alexander;Fraenkel, Aviezri S.;Weiss, BarakIterated Beatty functions.Random Comput. Dynam.1(1992/93),no. 3,333–348. (Reviewer: R. G. Stoneham)11B34 (11B75)
    Review PDFClipboardJournalArticle1 Citation
    MR1130685ReviewedBerger, M. A.;Felzenbaum, A.;Fraenkel, A. S.;Holzman, R.On infinite and finite covering systems.Amer. Math. Monthly98(1991),no. 8,739–742. (Reviewer: Anne Ludington Young)11B05 (11B50)
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    MR1119698ReviewedFraenkel, Aviezri S.;Lorberbom, MordechaiNimhoff games.J. Combin. Theory Ser. A58(1991),no. 1,1–25. (Reviewer: Daniel Elliott Loeb)90D46 (68Q25)
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    MR1095546IndexedFraenkel, Aviezri S.Selected bibliography on combinatorial games and some related material.Combinatorial games (Columbus, OH, 1990),191–226,Proc. Sympos. Appl. Math., 43,AMS Short Course Lecture Notes,Amer. Math. Soc., Providence, RI,1991.90D46 (05A99)
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    MR1095543IndexedFraenkel, Aviezri S.Complexity of games.Combinatorial games (Columbus, OH, 1990),111–153,Proc. Sympos. Appl. Math., 43,AMS Short Course Lecture Notes,Amer. Math. Soc., Providence, RI,1991.90D46 (05A99)
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    MR1095370ReviewedFraenkel, Aviezri S.;Scheinerman, Edward R.A deletion game on hypergraphs.ARIDAM III (New Brunswick, NJ, 1988).Discrete Appl. Math.30(1991),no. 2-3,155–162.90D43 (05C65)
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    MR1084184ReviewedFraenkel, A. S.;Porta, H.;Stolarsky, K. B.Some arithmetical semigroups.Analytic number theory (Allerton Park, IL, 1989),255–264,Progr. Math., 85,Birkhuser Boston, Boston, MA,1990. (Reviewer: F. Beukers)11A05 (20M14)
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    MR1081578ReviewedBerger, Marc A.;Felzenbaum, Alexander;Fraenkel, Aviezri S.Irreducible disjoint covering systems (with an application to Boolean algebra).First International Colloquium on Pseudo-Boolean Optimization and Related Topics (Chexbres, 1987).Discrete Appl. Math.29(1990),no. 2-3,143–164. (Reviewer: Ivan Korec)20D60 (03B05 03G05 11B25)
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    MR1080539ReviewedBlass, Uri;Fraenkel, Aviezri S.The Sprague-Grundy function for Wythoff's game.Theoret. Comput. Sci.75(1990),no. 3,311–333. (Reviewer: Jos Potters)90D43
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    MR1075260ReviewedFraenkel, A. S.;Klein, S. T.Bidirectional Huffman coding.Comput. J.33(1990),no. 4,296–307. (Reviewer: Alexander Barg)94A29
    Review PDFClipboardJournal7 Citations
    MR1031263ReviewedFraenkel, Aviezri S.;Lorberbom, MordechaiEpidemiography with various growth functions.Combinatorics and complexity (Chicago, IL, 1987).Discrete Appl. Math.25(1989),no. 1-2,53–71. (Reviewer: A. Pultr)90D05 (90D42 92A20)
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    MR1024962ReviewedFraenkel, A. S.;Harary, F.Geodetic contraction games on graphs.Internat. J. Game Theory18(1989),no. 3,327–338. (Reviewer: Prabir Das)90D05 (05C99)
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    MR1009869ReviewedDuvdevani, N.;Fraenkel, A. S.Properties ofk-Welter's game.Discrete Math.76(1989),no. 3,197–221. (Reviewer: Victor J. Baston)90D05 (05A99 90D42)
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    MR0992303ReviewedFraenkel, Aviezri S.The use and usefulness of numeration systems.Inform. and Comput.81(1989),no. 1,46–61.68Q20 (20F99)
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    MR0983032ReviewedAgur, Z.;Fraenkel, A. S.;Klein, S. T.Errata to: "The number of fixed points of the majority rule''.Discrete Math.73(1989),no. 3,321. (Reviewer: K. B. Reid)05A15 (68Q80 90A08 92A10 92A20)
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    MR0991211ReviewedBerger, Marc A.;Felzenbaum, Alexander;Fraenkel, Aviezri S.Mycielski-Sierpiński conjecture and Korec-Znm result.Colloq. Math.56(1988),no. 2,241–249. (Reviewer: Michael E. Mays)20D60 (11A07 20D50)
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    MR0957212ReviewedFraenkel, Aviezri S.;Loebl, Martin;Nes̆etr̆il, JaroslavEpidemiography. II. Games with a dozing yet winning player.J. Combin. Theory Ser. A49(1988),no. 1,129–144.90D42 (05C20 90D05)
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    MR0955126ReviewedAgur, Z.;Fraenkel, A. S.;Klein, S. T.The number of fixed points of the majority rule.Discrete Math.70(1988),no. 3,295–302. (Reviewer: K. B. Reid)05A15 (68Q80 90A08 92A10 92A20)
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    MR0945272ReviewedBerger, Marc A.;Felzenbaum, Alexander;Fraenkel, Aviezri S.Improvements to the Newman-Znm result for disjoint covering systems.Acta Arith.50(1988),no. 1,1–13. (Reviewer: Š. Znm)11A07 (11B25)
    Review PDFClipboardJournal4 Citations
    MR0945267ReviewedBerger, Marc A.;Felzenbaum, Alexander;Fraenkel, Aviezri S.Disjoint covering systems with precisely one multiple modulus.Acta Arith.50(1988),no. 2,171–182. (Reviewer: Š. Znm)11B25 (11A07)
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    MR0942479ReviewedBerger, Marc A.;Erdős, Paul;Felzenbaum, Alexander;Fraenkel, Aviezri S.Nearly disjoint covering systems.Eleventh British Combinatorial Conference (London, 1987).Ars Combin.25(1988),B,231–246. (Reviewer: R. C. Mullin)11A07
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    MR0939862ReviewedBerger, Marc A.;Felzenbaum, Alexander;Fraenkel, Aviezri S.Covers of product sets and the Korec-Znm result.European J. Combin.9(1988),no. 2,131–138. (Reviewer: Ivan Korec)11B25
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    MR0922566ReviewedBerger, Marc A.;Felzenbaum, Alexander;Fraenkel, AviezriRemark on the multiplicity of a partition of a group into cosets.Fund. Math.128(1987),no. 3,139–144. (Reviewer: F. Prez Monasor)20D60 (20D20)
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    MR0899900ReviewedFraenkel, Aviezri S.;Goldschmidt, ElishevaPSPACE-hardness of some combinatorial games.J. Combin. Theory Ser. A46(1987),no. 1,21–38. (Reviewer: Andreas Blass)68Q15 (05C20 90D05 90D42)
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    MR0899899ReviewedKahane, Joseph;Fraenkel, Aviezri S.k-Welter—a generalization of Welter's game.J. Combin. Theory Ser. A46(1987),no. 1,1–20. (Reviewer: Victor J. Baston)90D05 (05A99 90D42)
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    MR0893463ReviewedBerger, Marc A.;Felzenbaum, Alexander;Fraenkel, Aviezri S.Necessary condition for the existence of an incongruent covering system with odd moduli. II.Acta Arith.48(1987),no. 1,73–79. (Reviewer: Š. Znm)11A07
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    MR0891542ReviewedBerger, M. A.;Felzenbaum, A.;Fraenkel, A. S.Lattice parallelotopes and disjoint covering systems.Discrete Math.65(1987),no. 1,23–46. (Reviewer: Š. Znm)11B25 (11A07)
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    MR0887178ReviewedFraenkel, A. S.;Kotzig, A.Partizan octal games: partizan subtraction games.Internat. J. Game Theory16(1987),no. 2,145–154. (Reviewer: G. A. Heuer)90D05
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    MR0880165ReviewedApostolico, Alberto;Fraenkel, Aviezri S.Robust transmission of unbounded strings using Fibonacci representations.IEEE Trans. Inform. Theory33(1987),no. 2,238–245. (Reviewer: Andrea Sgarro)94B45 (94A29)
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    MR0875291ReviewedBerger, M. A.;Felzenbaum, A.;Fraenkel, A. S.A nonanalytic proof of the Newman-Znm result for disjoint covering systems.Combinatorica6(1986),no. 3,235–243. (Reviewer: Š. Znm)11B25 (11A07 11B83)
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    MR0867643ReviewedFraenkel, Aviezri S.;Yesha, YaacovThe generalized Sprague-Grundy function and its invariance under certain mappings.J. Combin. Theory Ser. A43(1986),no. 2,165–177. (Reviewer: Harold Reiter)90D42 (05C20)
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    MR0847297ReviewedBerger, Marc A.;Felzenbaum, Alexander;Fraenkel, AviezriNecessary condition for the existence of an incongruent covering system with odd moduli.Acta Arith.45(1986),no. 4,375–379. (Reviewer: Š. Znm)11A07
    Review PDFClipboardJournal1 Citation
    MR0846712ReviewedBerger, Marc A.;Felzenbaum, Alexander;Fraenkel, AviezriThe Herzog-Schnheim conjecture for finite nilpotent groups.Canad. Math. Bull.29(1986),no. 3,329–333. (Reviewer: E. I. Khukhro)20D60 (20D15)
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    MR0843471ReviewedBerger, Marc A.;Felzenbaum, Alexander;Fraenkel, Aviezri S.Disjoint covering systems of rational Beatty sequences.J. Combin. Theory Ser. A42(1986),no. 1,150–153. (Reviewer: Calvin T. Long)11B75 (11B83)
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    MR0818066ReviewedBerger, Marc A.;Felzenbaum, Alexander;Fraenkel, Aviezri S.New results for covering systems of residue sets.Bull. Amer. Math. Soc. (N.S.)14(1986),no. 1,121–126. (Reviewer: Štefan Porubsk)11B25
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    MR0824850ReviewedBerger, Marc A.;Felzenbaum, Alexander;Fraenkel, Aviezri S.Improvements to two results concerning systems of residue sets.Ars Combin.20(1985),69–82. (Reviewer: Š. Znm)11A07
    Review PDFClipboardJournalArticle4 Citations
    MR0815340ReviewedFraenkel, Aviezri S.The use and usefulness of numeration systems.Combinatorial algorithms on words (Maratea, 1984),187–203,NATO Adv. Sci. Inst. Ser. F: Comput. Systems Sci., 12,Springer, Berlin,1985. (Reviewer: D. A. Klarner)68Q20 (68P05 68R05)
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    MR0815339IndexedFraenkel, Aviezri S.;Klein, Shmuel T.Novel compression of sparse bit-strings—preliminary report.Combinatorial algorithms on words (Maratea, 1984),169–183,NATO Adv. Sci. Inst. Ser. F: Comput. Systems Sci., 12,Springer, Berlin,1985.68P99
    Review PDFClipboardChapter3 Citations
    MR0789177ReviewedFraenkel, Aviezri S.;Nes̆etr̆il, JaroslavEpidemiography.Pacific J. Math.118(1985),no. 2,369–381. (Reviewer: Klaus Lommatzsch)90D05 (05C20)
    Review PDFClipboard3 Citations
    MR0777556ReviewedFraenkel, Aviezri S.Systems of numeration.Amer. Math. Monthly92(1985),no. 2,105–114. (Reviewer: Torleiv Klve)11B37
    Review PDFClipboard103 Citations
    Berger, Marc A.;Felzenbaum, Alexander;Fraenkel, Aviezri S.Irreducible disjoint covering systems (with an application to Boolean algebra).First International Colloquium on Pseudo-Boolean Optimization and Related Topics (Chexbres, 1987).Discrete Appl. Math.29(1990),no. 2-3,143–164.
    Berger, Marc A.;Felzenbaum, Alexander;Fraenkel, Aviezri S.Mycielski-Sierpiński conjecture and Korec-Znm result.Colloq. Math.56(1988),no. 2,241–249.
    MR0945272ReviewedBerger, Marc A.;Felzenbaum, Alexander;Fraenkel, Aviezri S.Improvements to the Newman-Znm result for disjoint covering systems.Acta Arith.50(1988),no. 1,1–13. (Reviewer: Š. Znm)11A07 (11B25)
    Review PDFClipboardJournal4 Citations
    MR0945267ReviewedBerger, Marc A.;Felzenbaum, Alexander;Fraenkel, Aviezri S.Disjoint covering systems with precisely one multiple modulus.Acta Arith.50(1988),no. 2,171–182. (Reviewer: Š. Znm)11B25 (11A07)
    Review PDFClipboardJournal1 Citation
    MR0791023ReviewedFraenkel, Aviezri S.;Hammer, Peter L.Pseudo-Boolean functions and their graphs.Convexity and graph theory (Jerusalem, 1981),137–146,North-Holland Math. Stud., 87,Ann. Discrete Math., 20,North-Holland, Amsterdam,1984. (Reviewer: Pavol Hell)90C99 (05C99 06E30)
    Review PDFClipboard3 Citations
    MR0744489ReviewedBoshernitzan, M.;Fraenkel, A. S.A linear algorithm for nonhomogeneous spectra of numbers.J. Algorithms5(1984),no. 2,187–198. (Reviewer: Richard T. Bumby)11Y55 (68Q40)
    Review PDFClipboard9 Citations
    MR0742402ReviewedFraenkel, Aviezri S.Wythoff games, continued fractions, cedar trees and Fibonacci searches.Theoret. Comput. Sci.29(1984),no. 1-2,49–73.68Q20 (05A99 90D05)
    Review PDFClipboard25 Citations
    MR0732206ReviewedMor, M.;Fraenkel, A. S.Cayley permutations.Discrete Math.48(1984),no. 1,101–112. (Reviewer: M. Livingston)05A15 (05A05 05C05)
    Review PDFClipboard7 Citations
    MR0741904ReviewedFraenkel, Aviezri S.;Mor, MosheCombinatorial compression and partitioning of large dictionaries.Comput. J.26(1983),no. 4,336–343.68P99 (68R05)
    Review PDFClipboardJournal
    MR0732312ReviewedFraenkel, A. S.;Mor, M.;Perl, Y.Is text compression by prefixes and suffixes practical?Acta Inform.20(1983),no. 4,371–389.68U15 (94A29)
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    MR0727659ReviewedFraenkel, Aviezri S.Wythoff games, continued fractions, cedar trees and Fibonacci searches.Automata, languages and programming (Barcelona, 1983),203–225,Lecture Notes in Comput. Sci., 154,Springer, Berlin,1983.68Q20 (11B39 90D05)
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    MR0691047ReviewedMor, M.;Fraenkel, A. S.Permutation generation on vector processors.Comput. J.25(1982),no. 4,423–428.68E99 (05A05 68C05)
    Review PDFClipboardJournal
    MR0678172ReviewedFraenkel, A. S.;Yesha, Y.Theory of annihilation games. I.J. Combin. Theory Ser. B33(1982), no. 1, 60–86. (Reviewer: Selim G. Akl)90D05 (05C20)
    Review PDFClipboardJournal6 Citations
    MR0675171ReviewedFraenkel, L. E.On the embedding ofC1(Ω)inC0,α(Ω).J. London Math. Soc. (2)26(1982),no. 2,290–298. (Reviewer: J. S. Martins)46E35
    Review PDFClipboardJournal
    MR0671176ReviewedFraenkel, Aviezri S.;Tassa, UziStrategies for compounds of partizan games.Math. Proc. Cambridge Philos. Soc.92(1982),no. 2,193–204.90D05
    Review PDFClipboard3 Citations
    MR0666110ReviewedAmick, C. J.;Fraenkel, L. E.;Toland, J. F.On the Stokes conjecture for the wave of extreme form.Acta Math.148(1982),193–214. (Reviewer: Alberto Valli)35R35 (76B15)
    Review PDFClipboard116 Citations
    MR0660914ReviewedFraenkel, Aviezri S.How to beat your Wythoff games' opponent on three fronts.Amer. Math. Monthly89(1982),no. 6,353–361.90D05
    Review PDFClipboard56 Citations
    MR0675689ReviewedFraenkel, Aviezri S.Planar kernel and Grundy withd≤3,dout≤2,din≤2are NP-complete.Discrete Appl. Math.3(1981),no. 4,257–262.68C25 (05C20)
    Review PDFClipboard29 Citations
    MR0635143ReviewedFraenkel, Aviezri S.;Lichtenstein, DavidComputing a perfect strategy fornnchess requires time exponential inN.Automata, languages and programming (Akko, 1981),pp. 278–293, Lecture Notes in Comput. Sci., 115,Springer, Berlin-New York,1981.90D05 (68C25)
    Review PDFClipboardSeriesChapter5 Citations
    MR0629595ReviewedFraenkel, Aviezri S.;Lichtenstein, DavidComputing a perfect strategy fornnchess requires time exponential inn.J. Combin. Theory Ser. A31(1981),no. 2,199–214.68C25 (90D05)
    Review PDFClipboard11 Citations
    MR0616779ReviewedFraenkel, L. E.A lower bound for electrostatic capacity in the plane.Proc. Roy. Soc. Edinburgh Sect. A88(1981),no. 3-4,267–273.78A30 (31A15 49G05 52A40)
    Review PDFClipboard5 Citations
    MR0613413ReviewedBoshernitzan, M.;Fraenkel, A. S.Nonhomogeneous spectra of numbers.Discrete Math.34(1981),no. 3,325–327.10L10
    Review PDFClipboard11 Citations
    MR1572333DMLFraenkel, Aviezri S.; Herda, Hans;News and Letters.Math. Mag.53(1980),no. 1,59–61.
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    MR0593528ReviewedFraenkel, Aviezri S.From Nim to Go.Ann. Discrete Math.6(1980),137–156. (Reviewer: Harold Reiter)90D05 (05C20 68C25)
    Review PDFClipboardArticle1 Citation
  • MR1567093DMLFraenkel, Aviezri S.;Book Review: On numbers and games // Book Review: Surreal numbers.Bull. Amer. Math. Soc.84(1978),no. 6,1328–1336.
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    MR0523586ReviewedFraenkel, A. S.;Mushkin, M.;Tassa, U.Determination of[nθ]by its sequence of differences.Canad. Math. Bull.21(1978),no. 4,441–446. (Reviewer: Maurice Mignotte)10F20 (10A30)
    Review PDFClipboard18 Citations
    MR0496795ReviewedFraenkel, Aviezri S.;Tassa, Uzi;Yesha, YaacovThree annihilation games.Math. Mag.51(1978),no. 1,13–17. (Reviewer: Stanisław Zdrzałka)90D99
    Review PDFClipboard1 Citation
    MR0464779ReviewedAttar, R.;Choueka, Y.;Dershowitz, N.;Fraenkel, A. S.KEDMA—linguistic tools for retrieval systems.J. Assoc. Comput. Mach.25(1978),no. 1,52–66. (Reviewer: K. H. V. Booth)68A50
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    MR0429815ReviewedFraenkel, Aviezri S.Complementary systems of integers.Amer. Math. Monthly84(1977),no. 2,114–115. (Reviewer: Jau-Shyong Shiue)10L05 (10A40)
    Review PDFClipboard8 Citations
    MR0449726ReviewedFraenkel, A. S.;Yesha, Y.Theory of annihilation games.Bull. Amer. Math. Soc.82(1976),no. 5,775–777. (Reviewer: Richard K. Guy)90D05 (05C20)
    Review PDFClipboard4 Citations
    MR0414115ReviewedFraenkel, A. S.;Tassa, U.Strategy for a class of games with dynamic ties.Comput. Math. Appl.1(1975),no. 2,237–254. (Reviewer: Richard K. Guy)90D05
    Review PDFClipboard4 Citations
    MR0384171ReviewedFraenkel, A. S.;Perl, Y.Constructions in combinatorial games with cycles.Infinite and finite sets (Colloq., Keszthely, 1973; dedicated to P. Erdős on his 60th birthday), Vols. I, II, III,pp. 667–699. Colloq. Math. Soc. Jnos Bolyai, Vol. 10,North-Holland, Amsterdam,1975. (Reviewer: R. K. Guy)90D05 (05C20)
    Review PDFClipboardSeriesChapter5 Citations
    MR0376591ReviewedBorosh, I.;Fraenkel, A. S.A generalization of Jarnk's theorem on Diophantine approximations to Ridout type numbers.Trans. Amer. Math. Soc.211(1975),23–38. (Reviewer: Roland Fischer)10K15
    Review PDFClipboardJournal
    MR0374076ReviewedFraenkel, Aviezri S.Further characterizations and properties of exactly covering congruences.Discrete Math.12(1975),93–100; erratum, ibid.12(1975), no. 4, 397. (Reviewer: A. J. Zajta)10L05
    Review PDFClipboardJournal1 Citation
    MR0354027ReviewedFraenkel, Aviezri S.Combinatorial games with an annihilation rule.The influence of computing on mathematical research and education (Proc. Sympos. Appl. Math., Vol. 20, Univ. Montana, Missoula, Mont., 1973),pp. 87–91.Amer. Math. Soc., Providence, R.I.,1974. (Reviewer: T. L. Saaty)90D05
    Review PDFClipboardSeriesChapter3 Citations
    MR0339824ReviewedFraenkel, A. S.;Borosh, I.A generalization of Wythoff's game.J. Combinatorial Theory Ser. A15(1973),175–191. (Reviewer: Richard K. Guy)90D05
    Review PDFClipboardJournal14 Citations
    MR0316359ReviewedFraenkel, Aviezri S.A characterization of exactly covering congruences.Discrete Math.4(1973),359–366. (Reviewer: J. M. Gandhi)10A10 (10A35)
    Review PDFClipboardJournal6 Citations
    MR0309770ReviewedFraenkel, Aviezri S.Complementing and exactly covering sequences.J. Combinatorial Theory Ser. A14(1973),8–20. (Reviewer: A. Zajta)05B40
    Review PDFClipboardJournal30 Citations
    MR0308060ReviewedBorosh, I.;Fraenkel, A. S.A generalization of Jarnk's theorem on Diophantine approximations.Nederl. Akad. Wetensch. Proc. Ser. A75=Indag. Math.34(1972), 193–201. (Reviewer: W. W. Adams)10F10
    Review PDFClipboardJournalArticle17 Citations
    MR0302599ReviewedFraenkel, Aviezri S.;Levitt, Jonathan;Shimshoni, MichaelCharacterization of the set of valuesf(n)=[nα],n=1,2,⋯.Discrete Math.2(1972),no. 4,335–345. (Reviewer: R. E. Greenwood)10L10
    Review PDFClipboard10 Citations
    MR0321866ReviewedFraenkel, Aviezri S.Diophantine equations involving generalized triangular and tetrahedral numbers.Computers in number theory (Proc. Sci. Res. Council Atlas Sympos. No. 2, Oxford, 1969),pp. 99–114.Academic Press, London,1971. (Reviewer: J. Riordan)10A40 (10B35)
    Review PDFClipboardSeriesChapter
    MR0294157ReviewedFraenkel, A. S."Economic traversal of labyrinths'': Correction.Math. Mag.44(1971),12.05C35
    Review PDFClipboardJournal
    MR0265194ReviewedFraenkel, A. S.Economic traversal of labyrinths.Math. Mag.43(1970),125–130.05.40
    Review PDFClipboardJournal2 Citations
    MR0234900ReviewedFraenkel, Aviezri S.The bracket function and complementary sets of integers.Canadian J. Math.21(1969),6–27. (Reviewer: B. Garrison)10.05
    Review PDFClipboardJournal32 Citations
    MR0188159ReviewedFraenkel, A. S.;Borosh, I.Corrigendum: Fractional dimension of a set of transcendental numbers.Proc. London Math. Soc. (3)16(1966),192.10.32
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    MR0187379ReviewedBorosh, I.;Fraenkel, A. S.Exact solutions of linear equations with rational coefficients by congruence techniques.Math. Comp.20(1966),107–112. (Reviewer: B. N. Parlett)65.35
    Review PDFClipboardJournal6 Citations
    MR0177949ReviewedFraenkel, A. S.;Borosh, I.Fractional dimension of a set of transcendental numbers.Proc. London Math. Soc. (3)15(1965),458–470. (Reviewer: J. Popken)10.32
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    MR0170860ReviewedFraenkel, Aviezri S.Distance to the nearest integer and algebraic independence of certain real numbers.Proc. Amer. Math. Soc.16(1965),154–160. (Reviewer: W. J. LeVeque)10.32
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    MR0164932ReviewedFraenkel, Aviezri S.Transcendental numbers and a conjecture of Erdős and Mahler.J. London Math. Soc.39(1964),405–416. (Reviewer: G. J. Rieger)10.32
    Review PDFClipboard2 Citations
    MR0154841ReviewedFraenkel, Aviezri S.New proof of the generalized Chinese Remainder Theorem.Proc. Amer. Math. Soc.14(1963),790–791. (Reviewer: D. H. Lehmer)10.06 (10.09)
    Review PDFClipboardJournal1 Citation
    MR0153613ReviewedGordon, B.;Fraenkel, A. S.;Straus, E. G.On the determination of sets by the sets of sums of a certain order.Pacific J. Math.12(1962),187–196. (Reviewer: L. Moser)10.62 (10.05)
    Review PDFClipboardJournal4 Citations
    MR0146990ReviewedCantor, D. G.;Estrin, G.;Fraenkel, A. S.;Turn, R.A very high-speed digital number sieve.Math. Comp.16(1962),141–154. (Reviewer: D. H. Lehmer)68.00 (10.64)
    Review PDFClipboardJournal2 Citations
    MR0144852ReviewedFraenkel, Aviezri S.On a theorem of D. Ridout in the theory of Diophantine approximations.Trans. Amer. Math. Soc.105(1962),84–101. (Reviewer: J. Popken)10.30
    Review PDFClipboardJournal4 Citations
    MR2939204ThesisFraenkel, Aviezri S.RATIONAL APPROXIMATIONS TO ALGEBRAIC NUMBERS.Thesis (Ph.D.)–University of California, Los Angeles. 1961. (no paging),ProQuest LLC
    Review PDFClipboardSeries
    MR0122019ReviewedFraenkel, Aviezri S.The use of index calculus and Mersenne primes for the design of a high-speed digital multiplier.J. Assoc. Comput. Mach.8(1961),87–96. (Reviewer: C. B. Haselgrove)68.00
    Review PDFClipboardJournal1 Citation
    A.S. Fraenkel, Wythoff Games, Continued Fractions, Cedar Trees and Fibonacci Searches Theoretical Computer Science (1984) 49-73
  • A.S. Fraenkel and I. Borosh, A generalization of Wythoff's game, J. Combin. Theory, (1973) 175--191.
  • III. Hebrew Transliterated Reprints
  • A.S. Fraenkel, Eileh v'eileh, in Hebrew. 'Hama'ayan, July 2023.
  • A.S. Fraenkel, Midat ha'anava' at alit al kulana , in Hebrew; 'Hama'ayan, December 2022.
  • A.S. Fraenkel, T'guva Litguva Transliteration , in Hebrew; appeared in 'Hama'ayan, July 2022.
  • A.S. Fraenkel, Yachasey gomlin beyn Beth Din l'veyn mitdaynim, (in Hebrew). Appeared in "Hama'ayan", Chanuka, Tashpav, December 2021.
  • A.S. Fraenkel, Al hilchot hashacheyn hachiloni (in Hebrew). Hatzofe Erev shabbat Mas'ey, ha-tashsach, Aug. 1, 2008, p. 40.
  • A.S. Fraenkel, Sifrei Chayim v'sifrei Meitim P'tuchim lfanav (in Hebrew). Hama'ayan 48, Issue 1, Tishrei ha-tashsach, September 2007, pp. 34--37,
  • A.S. Fraenkel, Hirhurim m'atim al proyekt hashu''t (in Hebrew) {\it Hatzofe\/} Erev Shabbat Hagadol, 11 Nissan ha-tashsaz, March 30, 2007, pp. 11,14.
  • A.S. Fraenkel, Madua ein korin korban musaf shel shabbat b'shabbat -- B, in Hebrew. Hama'ayan 47, Issue 3, Nissan Ha-Tashsaz, March 2007, pp. 25--29.
  • A.S. Fraenkel, Al t'filot ha'amida shel arvit, shacharit, mincha umisfei rosh chodesh, in Hebrew. Moriya 27, Issue 9-10, pp. 85--89, Tevet Ha-tashsav, Jan 2006.
  • A.S. Fraenkel, Korban pesach b'veit hamikdash: She'elat z'man umakom, in Hebrew. Sefer hazikaron ``Yoseif Da'at" l'zichro shel Yoseif Aharon Nitzan za"l (Memorial volume commemorating the memory of the late Yosef Aharon Nitzan), Sh'vat Ha-tashsav (Feb 2006), pp. 238--244.
  • A.S. Fraenkel, Vaykonein Yirm'yahu al Yoshiyahu, in Hebrew. Hatzofe Erev Shabbat Pinchas, ha-tashsad, July 9, 2004, p. 14.
  • A.S. Fraenkel, Mikra'ot b'chag hashavu'ot v'darchei heyseik (in Hebrew). Dedicated to the memory of Prof. Shalom (Freddy) Hirshfeld, za''l, Hatzofe Erev Chag Hashavuot, ha-tashsad, May 25, 2004, p. 13.
  • A.S. Fraenkel, Meshech Chochma l'sar haTorah, in Hebrew. Dedicated to the memory of Dr. Zvi Betzer, za"l, Hatzofe Erev Shabbat Ki Tavo, ha-tashsag, Sept 12, 2003, p. 12, 14
  • A.S. Fraenkel, Sukkot B'Shavu'ot, in Hebrew. Hatzofe Erev Shabbat Sh'lach-L'cha, ha-tashsag, June 20, 2003, p. 14
  • A.S. Fraenkel, hitmachut, mumchiyut utchumim, in Hebrew. Hatzofe Erev Shabbat Vayeishev, erev chag haChanukah, ha-tashsag, Nov 29, 2002, p. 11.
  • S. Yedid and A.S. Fraenkel, Hashofeit kol ha'aretz lo ya'aseh mishpat?, in Hebrew. Dedicated to the memory of Dr. Zvi Betzer, za"l, Hatzofe Erev Shabbat Vayeira, ha-tashsag, Oct 25, 2002, p. 14.
  • A.S. Fraenkel, R'galim, korbanot, avodah zarah, in Hebrew. Hatzofe Erev chag haSukkot, ha-tashsag, Sept 20, 2002, p. 13.
  • A.S. Fraenkel, Bein yachid l'tzibbur biymei din, in Hebrew. Hatzofe 1st part: Erev Rosh Hashanah, ha-tashsag, Sept 6, 2002, pp. 12--13; 2nd part: Erev Yom Kippur, Sept 15, 2002, p. 4.
  • A.S. Fraenkel, He'arot z'irot (2), in Hebrew. Hatzofe (under the title "Zeicheir liy'tzi'at mitzrayim") Erev Shabbat Hagadol, 13 Nissan, ha-tashsa; April 4, 2001, pp. 12-13.
  • A.S. Fraenkel He'arot z'irot (1), in Hebrew. Hatzofe Erev Shabbat Mishpatim, parashat Sh'kalim, 1 Adar, ha-tashsa; Feb 23, 2001, pp. 14-15.
  • A.S. Fraenkel M'sirut nefesh ugvurat nefesh, in Hebrew. Hatzofe Erev Shabbat Bo, 9 Sh'vat, ha-tashsa; Feb 2, 2001, p. 10.
  • A.S. Fraenkel Al ``Meshech Chochma'', in Hebrew. Hatzofe (under the title 'Bein n'vuat emet linvuat sheker (al echad meiekronot haparshanut shel ha"meshech chochmah")', Erev Shabbat Tol'dot, 4 Kisleiv ha-tashsa; Dec 1, 2000, p. 8.
  • A.S. Fraenkel, Bein yehudim lishe'einam yehudim, in Hebrew. Hatzofe, Appeared in two parts: Erev Shavuot, 5 Sivan ha-tashas, June 8, 2000; and Erev Shabbat B'ha'alotcha, 13 Sivan ha-tashas; June 16, 2000.
  • A.S. Fraenkel, Simaniyot baMikra, in Hebrew. Hatzofe, Erev Shabbat K'doshim, 30 Nissan ha-tashas; May 5, 2000.
  • A.S. Fraenkel, Hadramah hashnatit, in Hebrew. Hatzofe, Erev Shabbat Vayigash, 8 Teiveit ha-tashas; Dec. 17, 1999, p. 12.
  • A.S. Fraenkel, T'filah: keifel teivot umiktzat hanhagot shel shatz, in Hebrew. Hatzofe, Erev Rosh Hashanah ha-tashas, 29 Elul ha-tashnat; Sept. 10, 1999, pp. 16--17.
  • A.S. Fraenkel, Chidon otzrot yisraeil, in Hebrew. In Memorial Volume commemorating Rabbi Aaron Nathan Weiss zatzal. A preliminary version appeared in Hatzofe, Erev Shabbat Bamidbar, Yom Shichrur Yerushalayim, 28 Iyar ha-tashnat; May 14, 1999. p. 14.
  • A.S. Fraenkel, Kabalat ol malchut shamayim, in Hebrew. Morashteinu vol. 13, 33-38, Sept. 1999. Preliminaty version appeared in Hatzofe, Erev Shabbat Vay'chi, 13 Teiveit ha-tashnat; January 1, 1999, p. 12.
  • A.S. Fraenkel, K'az kein atah, in Hebrew. Hatzofe, Erev Pesach, 14 Nissan ha-tashnat; March 31, 1999, p. 14.
  • A.S. Fraenkel, Bameh maftirin uvameh ein maftirin, in Hebrew. Hatzofe, Erev Shabbat Nitzavim-Vayeilech, 24 Elul ha-tashnaz; September 26, 1997, pp. 7--8.
  • A.S. Fraenkel, Madua ein korin korban musaf shel shabbat b'shabbat, in Hebrew. Hatzofe, Erev Shabbat Pin'chas, 20 Tamuz ha-tashnaz; July 25, 1997, p. 6.
  • A.S. Fraenkel, Hafradat rashuyot tifkudit bein kohen gadol, melech v'sarim?, in Hebrew. Hatzofe, Erev Shabbat Acharei Mot, 25 Nissan ha-tashnaz; May 2, 1997, p. 7.
  • A.S. Fraenkel, Haramba"m, haRashb"a uMaran al ta'ut b'seifer Torah, in Hebrew. Moriya 21 Issue 5--6, Adar Beit ha-tashnaz; 1997, pp. 109--110.
  • A.S. Fraenkel, L'olam heveih adam koneis divrei Torah k'lalim, in Hebrew. Hatzofe, Erev Shabbat Ki Tissa, 21 Adar Aleph ha-tashnaz; Feb. 28, 1997, p. 8.
  • A.S. Fraenkel, Nusach birkat "me'ein shalosh" utfilato shel kohen gadol b'yom hakipurim, in Hebrew. Sh'ma'atin 125, Chanukah ha-tashnav; 1995, pp. 80-87.

  • Games Bibliography

    A dynamic bibliography on Combinatorial Games, currently containing over 1700 items is a Dynamic Survey (D2, originally 1994) in the Dynamic Surveys section of the Electronic Journal of Combinatorics. For the latest update, view/download one of the files: gb.dvi, gb.pdf. Corrections, suggestions and comments are welcome. They should be sent to me by email.

    • Electronic Journals

    Some of the leading refereed electronic journals in mathematics can be accessed from here, via the courtesy of the AMS. We mention especially the influential Electr. J. Combinatorics, and the younger, yet prestigeous, INTEGERS -- Electronic Journal of Combinatorial Number Theory. It has a combinatorial games section.

    The Responsa Storage and Retrieval Project

    The Responsa Project stores the largest compilation of Jewish databases (it should actually be considerably larger). The most sophisticated search tools for Hebrew and Aramaic text processing (which should be much more sophisticated!) have been developed for searching it. Its philosophy, described from two viewpoints, can be found at: Yaacov Choueka, Aviezri Fraenkel's Work in Information Retrieval and Related Areas, A.S. Fraenkel, The Responsa storage and retrieval system---whither? The Hebrew version: Proyect hashut: avar, hoveh---v'gam atid? appeared in Dinei Yisrael 19 (1997-98) 253--270. It is a full text storage and retrival system, preceeding Google by 35 years, used worldwide. In 2007 it was awarded the prestigious Israel Prize.

    • The Good Countries and the Good People Therein

  • Australia: Rony Attar, Nhan Bao Ho, Jamie Simpson
  • Belgium; Emilie Charlier, Michel Rigo
  • Canada: Jason Bell, British Columbia; James Jones, Alberta; the late Anton Kotzig, Quebec; Richard Nowakowski, Nova Scotia; Gert Sabidussi, Quebec
  • China: Rudolf Fleischer, Haiyan Li, Sanyang Liu, Wen An Liu
  • Czech Republic: Martin Loebl, Jaroslav Nesetril
  • France; Eric Duchene, Sylvain Gravier
  • Germany: Sandor Fekete, Matthias Schmitt
  • Hungary: the late Paul Erdos, Vera Sos
  • Israel: Zvia Agur, Shiri Artstein-Avidan, Alexander Barabash, Marc Berger, Uri Blass, Viktor Bronstein, Yaacov Choueka, Meir Cohen, Nachum Dershowitz, Joseph Dueck, N. Duvdevani, the late Joseph Gillis, Lior Goldberg, Elisheva Goldschmidt, Romina Guelman, Ron Holzman, Tomi Klein, Dalia Krieger, the late Dan Loewenthal, Mordechai Lorberbom, the late Moshe Mor, Mordechai Mushkin, Michal Ozery, Udi Peled, Ofer Rahat, Benny Reuter, D. Schindler, Tamar Seeman, E. Segal, the late Michael Shimshoni, Mark Slae, E. Spitz, Yuval Tanny, Uzi Tassa, Barak Weiss, Sinai Yedid (Responsa), Dmitri Zusman
  • Italy: The late Alberto Apostolico
  • Portugal: Carlos Santos
  • Sweden: Peter Hegarty, Urban Larsson
  • UK: Jonathan Levitt, Mike Paterson
  • USA: George Andrews, PA, Saul Blanco, Itshak Borosh, TX; Michael Boshernitzan, TX; the late David Cantor, CA; Philip J. Davis, RI; Erik Demaine, MA; Roger Eggleton, IL; the late Gerald Estrin, CA; Alexander Felzenbaum, NY; Alex Fink, NC; Michael Garey, NJ; the late Basil Gordon, CA; Vladimir Gurvich, NJ; the late Peter Hammer, NJ; the late Frank Harary, NM; Robert Hearn, CA, Hans Herda, MA; Alan Jaffrey, IL; David Johnson, NJ; Joseph Kahane, NY; Clark Kimberling, IN; Alex Kontorovich, NY; David Lichtenstein, MA; Yehoshua Perl, NJ; Horacio Porta, IL; D. Raab, NY; Edward Reingold, IL; Elnatan Reisner, MD; Prashant Saxena, IL;Thomas Schaefer, CA; Edward Scheinerman, MD; James Sellers, PA, Aaron Siegel, CA, Shai Simonson, MA; Kenneth Stolarsky, IL; the late Ernst Straus, CA; the late Rein Turn, CA; Daniel Ullman, DC; Yaacov Yesha, MD

  • Vanity of vanities -- all is vanity (Eccl. 1,2)

    2014, Medal of Honor World Orthodox Leadership Forum, for the Responsa Project. Rabbi Avichai Katzin, from the awarding committee, wrote inter alia (translation from Hebrew): "The establishment of an enterprise as important as the Responsa Project, that daily grants many thousands the study of Judaica at an outstanding scale, undoubtely deserves more than the decoration you received."
  • 2007, Elected Meritocrat of Rehovot (Yakir Ha'ir). One of the photos of the ceremony, March 6, 2007. (without recipient and spouse)
  • 2007, Israel Prize for the Responsa Project, initiated in 1963, that appears to be the first viable, durable full-text retrieval system, 35 years prior to Google.
  • 2006, Recipient of WEIZAC Medal, at December 5 special seminar, celebrating recognition by the IEEE of the WEIZAC project as a Milestone in the History of Computers. (WEIZAC, constructed at the Weizmann Institute of Science in 1954, was the first electronic digital computer in the Middle East, and one of the first in the world.)
  • 2005, Euler Medal recipient of the Institute for Combinatorics and Its Applications. Excerpts from the citation in Bull. ICA 47, May 2006; front of medal, back; photographed by Eli Shechtman.
  • 2005, Runner up in European Mathematical Society Article Competition.
  • 2001, The Fraenkel Festschrift volume, Electr, J. of Combinatorics, vol. 8(2).
  • 1998, Quality Initiative Citation to the Responsa Project for creative, high-quality and visionary projects to celebrate the 50th anniversary of the establishment of the State of Israel.
  • 1972, Feder Foundation Prize for initiating and creating the Responsa Project.
  • Wikipedia pages: Hebrew ; English ; German .

  • Personal Data

  • Email: "aviezri.fraenkel" followed by the "at" symbol, followed by "weizmann.ac.il" .
  • Telephone: 972-8-9343539; secretary: 972-8-9343545
  • Fax: 972-8-9342945.
  • Business address:
  • Professor Aviezri S. Fraenkel
  • Dept of Compu Sci & Appl Math
  • Weizmann Institute of Science
  • 76100 Rehovot
  • Israel
  • URL for this homepage is: http://www.wisdom.weizmann.ac.il/~fraenkel
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