Aviezri Fraenkel's Home Page

I. Some Preprints

II. English Reprints

III. Hebrew Transliterated Reprints

I. Some Preprints

• A. Amir, O. Amir, A.S. Fraenkel, D. Sarne, On the Practical Power of the KMP Automaton ,

• D.Klein and A.S.Fraenkel, K-Pile Wythoff Games, Lexicographic Wythoff, to appear in Games Without Chance.

• A.S. Fraenkel,Complementary balanced words over an arbitrary finite alphabet.

• A.S. Fraenkel, Im Hatzibur, l'ma'an hazulat, in Hebrew.

• 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 rosh 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 

  • 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. Monthly 98 (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.

MR4363103 Reviewed Fraenkel, Aviezri S. Patrolling the border of a striking conjecture. Integers 22 (2022), Paper No. A3, 6 pp. 11B75

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MR4188748 Reviewed Fraenkel, Aviezri S.; Larsson, Urban Games on arbitrarily large rats and playability. Integers 19 (2019), Paper No. G04, 29 pp. (Reviewer: Grant Cairns) 91A46 (05A17 11B75)

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MR3965376 Reviewed Fraenkel, Aviezri S.; Larsson, Urban Take-away games on Beatty's theorem and the notion of k-invariance. Games of no chance 5, 333–342, Math. Sci. Res. Inst. Publ., 70, Cambridge Univ. Press, Cambridge, 2019. 91A46

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MR3965364 Reviewed Duchêne, Eric; Fraenkel, Aviezri S.; Gurvich, Vladimir; Ho, Nhan Bao; Kimberling, Clark; Larsson, Urban Wythoff visions. Games of no chance 5, 35–87, Math. Sci. Res. Inst. Publ., 70, Cambridge Univ. Press, Cambridge, 2019. 91A46 (91-02)

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MR3842044 Reviewed Goldberg, Lior; Fraenkel, Aviezri S. Rulesets for Beatty games. Internat. J. Game Theory 47 (2018), no. 2, 577–594. 91A46

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MR3842035 Indexed Fraenkel, Aviezri; Larsson, Urban; Santos, Carlos P.; von Stengel, Bernhard Special issue on combinatorial game theory. Internat. J. Game Theory 47 (2018), no. 2, 375–377. 91-06 (91A46)

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MR3784788 Reviewed Goldberg, 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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MR3661410 Reviewed Li, Haiyan; Liu, Sanyang; Fraenkel, Aviezri S.; Liu, Wen An Variants of (s,t)-Wythoff's game. Discrete Appl. Math. 227 (2017), 1–12. (Reviewer: Grant Cairns) 91A46

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MR3404489 Reviewed Andrews, George E.; Fraenkel, Aviezri S.; Sellers, James A. m-ary partitions with no gaps: a characterization modulo m. Discrete Math. 339 (2016), no. 1, 283–287. 05A17 (05A15 11P81)

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MR3560331 Reviewed Fraenkel, 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

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MR3560330 Reviewed Fraenkel, Aviezri S.; Peled, Udi Harnessing 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

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MR3418210 Reviewed Andrews, George E.; Fraenkel, Aviezri S.; Sellers, James A. Characterizing the number of m-ary partitions modulo m. Amer. Math. Monthly 122 (2015), no. 9, 880–885. (Reviewer: David M. Bressoud) 05A17 (11P83)

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MR3361813 Reviewed Fraenkel, Aviezri S.; Ho, Nhan Bao When are translations of P-positions of Wythoff's game P-positions? Integers 15A (2015), Paper No. A4, 12 pp. (Reviewer: Paweł Prałat) 91A46 (91A05)

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MR3233468 Indexed Fraenkel, Aviezri S.; Simpson, Jamie Corrigendum 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)

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MR3197293 Reviewed Fink, Alex; Fraenkel, Aviezri S.; Santos, Carlos LIM is not slim. Internat. J. Game Theory 43 (2014), no. 2, 269–281. (Reviewer: Nhan Bao Ho) 91A46 (68Q80)

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MR3363969 Reviewed Fraenkel, 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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MR3220917 Indexed Fraenkel, Aviezri S.; Tanny, Yuval A class of Whythoff-like games [reprint of MR3055681]. Combinatorial number theory, 91–107, De Gruyter Proc. Math., De Gruyter, Berlin, 2013. 91A46

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MR3055681 Reviewed Fraenkel, Aviezri; Tanny, Yuval A class of Wythoff-like games. Integers 12B (2012/13), Proceedings of the Integers Conference 2011, Paper No. A7, 18 pp. (Reviewer: Nhan Bao Ho) 91A46

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MR2897480 Reviewed Fraenkel, Aviezri S. RATWYT. College Math. J. 43 (2012), no. 2, 160–164. 91A46 (11B75 91A26)

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MR2852506 Indexed Fraenkel, Aviezri S. The vile, dopey, evil and odious game players. Discrete Math. 312 (2012), no. 1, 42–46. 91A46

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MR2988066 Reviewed Blanco, Saúl A.; Fraenkel, Aviezri S. Tromping games: tiling with trominoes. Integers 11 (2011), no. 3, 333–362. (Reviewer: Grant Cairns) 91A46 (05B50)

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MR2830984 Reviewed Fraenkel, Aviezri S. Aperiodic subtraction games. Electron. J. Combin. 18 (2011), no. 2, Paper 19, 12 pp. (Reviewer: Peter Vincent Hegarty) 91A46 (11B75 68Q25 91A05)

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MR2796920 Reviewed Larsson, Urban; Hegarty, Peter; Fraenkel, Aviezri S. Invariant and dual subtraction games resolving the Duchêne-Rigo conjecture. Theoret. Comput. Sci. 412 (2011), no. 8-10, 729–735. (Reviewer: András Sándor Pluhár) 91A46

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MR2681526 Indexed Fraenkel, Aviezri S. From enmity to amity. Amer. Math. Monthly 117 (2010), no. 7, 646–648. 11B83

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MR2661423 Reviewed Fraenkel, 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)

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MR2604147 Indexed Davis, Philip J.; Fraenkel, Aviezri S. Remembering Philip Rabinowitz [reprint of MR2361163]. The birth of numerical analysis, 179–186, World Sci. Publ., Hackensack, NJ, 2010. 65-03 (01A70 65D30)

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MR2600974 Reviewed Duchêne, Eric; Fraenkel, Aviezri S.; Nowakowski, Richard J.; Rigo, Michel Extensions and restrictions of Wythoff's game preserving its P positions. J. Combin. Theory Ser. A 117 (2010), no. 5, 545–567. (Reviewer: Thane Earl Plambeck) 91A46 (91A43)

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MR2572876 Reviewed Bell, Jason; Charlier, Emilie; Fraenkel, Aviezri S.; Rigo, Michel A 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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MR2526997 Reviewed Duchêne, 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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MR2438162 Reviewed Artstein-Avidan, Shiri; Fraenkel, Aviezri S.; Sós, 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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MR2379074 Reviewed Fraenkel, Aviezri S. Games played by Boole and Galois. Discrete Appl. Math. 156 (2008), no. 4, 420–427. 91A46

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MR2361163 Indexed Davis, Philip J.; Fraenkel, Aviezri S. Remembering Philip Rabinowitz. Notices Amer. Math. Soc. 54 (2007), no. 11, 1502–1506. 01A70

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MR2337048 Reviewed Fraenkel, Aviezri S.; Kontorovich, Alex The 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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MR2337047 Reviewed Fraenkel, Aviezri S. The Raleigh game. Combinatorial number theory, 199–208, de Gruyter, Berlin, 2007. (Reviewer: E. J. Barbeau) 91A46 (91A05)

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MR2184445 Reviewed Fraenkel, Aviezri S. Euclid and Wythoff games. Discrete Math. 304 (2005), no. 1-3, 65–68. 91A05 (91A46)

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MR2111926 Reviewed Fraenkel, Aviezri S.; Simpson, Jamie An extension of the periodicity lemma to longer periods. Discrete Appl. Math. 146 (2005), no. 2, 146–155. 68R15 (05A05)

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MR2116012 Reviewed Fraenkel, Aviezri S. New games related to old and new sequences. Integers 4 (2004), G6, 18 pp. (Reviewer: David Damanik) 11B83 (91A05)

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MR2056945 Indexed Demaine, 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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MR2056935 Indexed Fraenkel, 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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MR2056934 Reviewed Fekete, Sándor P.; Fleischer, Rudolf; Fraenkel, Aviezri; Schmitt, Matthias Traveling 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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MR2042724 Indexed Fraenkel, 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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MR2020683 Reviewed Fraenkel, Aviezri S.; Krieger, Dalia The 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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MR1973111 Indexed Fraenkel, 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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MR1973018 Reviewed Fraenkel, 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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MR1954732 Reviewed Fraenkel, 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, János Bolyai Math. Soc., Budapest, 2002. 68R15 (05A05)

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MR1909611 Indexed Fraenkel, 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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MR1909052 Reviewed Fraenkel, 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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MR1904570 Indexed Fraenkel, Aviezri S.; Simpson, Jamie An 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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MR1853261 Reviewed Fraenkel, Aviezri S.; Seeman, Tamar; Simpson, Jamie The 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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MR1806223 Reviewed Fraenkel, Aviezri S.; Rahat, Ofer Infinite cyclic impartial games. Computer and games (Tsukuba, 1998). Theoret. Comput. Sci. 252 (2001), no. 1-2, 13–22. 91A43 (05C20)

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MR1806222 Reviewed Fraenkel, Aviezri S.; Zusman, Dmitri A new heap game. Computer and games (Tsukuba, 1998). Theoret. Comput. Sci. 252 (2001), no. 1-2, 5–12. 91A46 (68T20)

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MR1798313 Reviewed Fraenkel, 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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MR1781301 Reviewed Fraenkel, Aviezri S. On the recurrence fm+1=bmfm−fm−1 and applications. Discrete Math. 224 (2000), no. 1-3, 273–279. (Reviewer: Vichian Laohakosol) 39A10 (11A55 40A15)

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MR1715689 Reviewed Fraenkel, Aviezri S.; Rahat, Ofer Infinite 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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MR1715688 Reviewed Fraenkel, Aviezri S.; Zusman, Dmitri A 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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MR1688708 Reviewed Fraenkel, 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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MR1687768 Reviewed Fraenkel, Aviezri S.; Simpson, Jamie The exact number of squares in Fibonacci words. WORDS (Rouen, 1997). Theoret. Comput. Sci. 218 (1999), no. 1, 95–106. (Reviewer: Patrice Séébold) 68R15 (11B39)

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MR1543394 DML Fraenkel, Aviezri; Martin, Reiner; Problems and Solutions: Solutions: Sets with Fixed Nim-Sum: 10564. Amer. Math. Monthly 106 (1999), no. 1, 71–72.

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MR1681514 Reviewed Fraenkel, Aviezri S. Heap games, numeration systems and sequences. Ann. Comb. 2 (1998), no. 3, 197–210. 91A05 (05A99 91A46)

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MR1656919 Reviewed Fraenkel, Aviezri S. Multivision: an intractable impartial game with a linear winning strategy. Amer. Math. Monthly 105 (1998), no. 10, 923–928. (Reviewer: E. Marchi) 90D46 (05A99)

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MR1652900 Reviewed Blass, Uri; Fraenkel, Aviezri S.; Guelman, Romina How far can nim in diguise be stretched? J. Combin. Theory Ser. A 84 (1998), no. 2, 145–156. (Reviewer: P. A. Biryukov) 91A46 (05A99)

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MR1638601 Reviewed Fraenkel, Aviezri S.; Ozery, Michal Adjoining to Wythoff's game its P-positions as moves. Theoret. Comput. Sci. 205 (1998), no. 1-2, 283–296. (Reviewer: P. A. Biryukov) 90D46

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MR1616571 Reviewed Fraenkel, Aviezri S.; Simpson, Jamie How many squares can a string contain? J. Combin. Theory Ser. A 82 (1998), no. 1, 112–120. 68R15 (11B85)

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MR1608392 Reviewed Fraenkel, Aviezri S.; Simpson, Jamie; Paterson, Mike On 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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MR1542936 DML Fraenkel, 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. Monthly 104 (1997), no. 1, 68–69.

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MR1444157 Reviewed Fraenkel, 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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MR1427984 Indexed Fraenkel, 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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MR1427980 Reviewed Fraenkel, 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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MR1427955 Reviewed Fraenkel, 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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MR1364104 Reviewed Jones, J. P.; Fraenkel, A. S. Complexities of winning strategies in Diophantine games. J. Complexity 11 (1995), no. 4, 435–455. (Reviewer: John Michael Robson) 68Q25 (03D15 68Q15 90D46)

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MR1336680 Reviewed Fraenkel, Aviezri S.; Loebl, Martin Complexity of circuit intersection in graphs. Discrete Math. 141 (1995), no. 1-3, 135–151. (Reviewer: Patrick Solé) 05C85 (57M25)

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MR1335685 Reviewed Fraenkel, Aviezri S.; Jaffray, Alan; Kotzig, Anton; Sabidussi, Gert Modular Nim. Theoret. Comput. Sci. 143 (1995), no. 2, 319–333. (Reviewer: Edward W. Packel) 90D05 (00A08 05A99 90D42)

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MR1310736 Reviewed Fraenkel, Aviezri S.; Holzman, Ron Gap problems for integer part and fractional part sequences. J. Number Theory 50 (1995), no. 1, 66–86. (Reviewer: Robert F. Tichy) 11J71 (11K31)

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MR1309124 Reviewed Fraenkel, Aviezri S.; Simpson, R. Jamie How many squares must a binary sequence contain? Electron. J. Combin. 2 (1995), Research Paper 2, approx. 9 pp. (Reviewer: Ákos Pintér) 11B83 (05A99)

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MR1670621 Indexed Fraenkel, 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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MR1310872 Reviewed Fraenkel, 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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MR1289489 Reviewed Fraenkel, A. S.; Klein, S. T. Complexity aspects of guessing prefix codes. Algorithmica 12 (1994), no. 4-5, 409–419. (Reviewer: Andrea Sgarro) 94A60 (68P25 68Q15 94A29 94A45)

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MR1274978 Reviewed Bronstein, Victor; Fraenkel, Aviezri S. On a curious property of counting sequences. Amer. Math. Monthly 101 (1994), no. 6, 560–563. (Reviewer: Giuseppe Pellegrino) 05A16

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MR1269166 Reviewed Fraenkel, Aviezri Even kernels. Electron. J. Combin. 1 (1994), Research Paper 5, approx. 13 pp. (Reviewer: Hans L. Bodlaender) 05C70 (68Q25 68R10)

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MR1264482 Reviewed Fraenkel, A. S.; Kimberling, Clark Generalized Wythoff arrays, shuffles and interspersions. Discrete Math. 126 (1994), no. 1-3, 137–149. (Reviewer: Volker Strehl) 11B83 (05A99)

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MR1138949 Reviewed Fraenkel, Aviezri S. Iterated floor function, algebraic numbers, discrete chaos, Beatty subsequences, semigroups. Trans. Amer. Math. Soc. 341 (1994), no. 2, 639–664. (Reviewer: Štefan Porubský) 11B83 (11B39 11Z50 58F13)

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MR1216328 Reviewed Fraenkel, Aviezri S.; Scheinerman, Edward R.; Ullman, Daniel Undirected edge geography. Theoret. Comput. Sci. 112 (1993), no. 2, 371–381. 90D35 (68Q25)

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MR1210094 Reviewed Eggleton, Roger B.; Fraenkel, Aviezri S.; Simpson, R. Jamie Beatty sequences and Langford sequences. Graph theory and combinatorics (Marseille-Luminy, 1990). Discrete Math. 111 (1993), no. 1-3, 165–178. (Reviewer: Š. Znám) 11B25 (05A10)

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MR1208665 Reviewed Fraenkel, A. S.; Simonson, S. Geography. Theoret. Comput. Sci. 110 (1993), no. 1, 197–214. 90D40 (05C85 68Q25 68R10 90D35)

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MR1148023 Reviewed Fraenkel, Aviezri S.; Simpson, R. Jamie On infinite disjoint covering systems. Proc. Amer. Math. Soc. 119 (1993), no. 1, 5–9. (Reviewer: Š. Znám) 11B25

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MR1214102 Reviewed Barabash, Alexander; Fraenkel, Aviezri S.; Weiss, Barak Iterated Beatty functions. Random Comput. Dynam. 1 (1992/93), no. 3, 333–348. (Reviewer: R. G. Stoneham) 11B34 (11B75)

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MR1130685 Reviewed Berger, M. A.; Felzenbaum, A.; Fraenkel, A. S.; Holzman, R. On infinite and finite covering systems. Amer. Math. Monthly 98 (1991), no. 8, 739–742. (Reviewer: Anne Ludington Young) 11B05 (11B50)

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MR1119698 Reviewed Fraenkel, Aviezri S.; Lorberbom, Mordechai Nimhoff games. J. Combin. Theory Ser. A 58 (1991), no. 1, 1–25. (Reviewer: Daniel Elliott Loeb) 90D46 (68Q25)

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MR1095546 Indexed Fraenkel, 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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MR1095543 Indexed Fraenkel, 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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MR1095370 Reviewed Fraenkel, 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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MR1084184 Reviewed Fraenkel, A. S.; Porta, H.; Stolarsky, K. B. Some arithmetical semigroups. Analytic number theory (Allerton Park, IL, 1989), 255–264, Progr. Math., 85, Birkhäuser Boston, Boston, MA, 1990. (Reviewer: F. Beukers) 11A05 (20M14)

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MR1081578 Reviewed 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. (Reviewer: Ivan Korec) 20D60 (03B05 03G05 11B25)

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MR1080539 Reviewed Blass, 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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MR1075260 Reviewed Fraenkel, A. S.; Klein, S. T. Bidirectional Huffman coding. Comput. J. 33 (1990), no. 4, 296–307. (Reviewer: Alexander Barg) 94A29

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MR1031263 Reviewed Fraenkel, Aviezri S.; Lorberbom, Mordechai Epidemiography 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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MR1024962 Reviewed Fraenkel, A. S.; Harary, F. Geodetic contraction games on graphs. Internat. J. Game Theory 18 (1989), no. 3, 327–338. (Reviewer: Prabir Das) 90D05 (05C99)

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MR1009869 Reviewed Duvdevani, N.; Fraenkel, A. S. Properties of k-Welter's game. Discrete Math. 76 (1989), no. 3, 197–221. (Reviewer: Victor J. Baston) 90D05 (05A99 90D42)

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MR0992303 Reviewed Fraenkel, Aviezri S. The use and usefulness of numeration systems. Inform. and Comput. 81 (1989), no. 1, 46–61. 68Q20 (20F99)

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MR0983032 Reviewed Agur, 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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MR0991211 Reviewed Berger, Marc A.; Felzenbaum, Alexander; Fraenkel, Aviezri S. Mycielski-Sierpiński conjecture and Korec-Znám result. Colloq. Math. 56 (1988), no. 2, 241–249. (Reviewer: Michael E. Mays) 20D60 (11A07 20D50)

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MR0957212 Reviewed Fraenkel, Aviezri S.; Loebl, Martin; Nes̆etr̆il, Jaroslav Epidemiography. II. Games with a dozing yet winning player. J. Combin. Theory Ser. A 49 (1988), no. 1, 129–144. 90D42 (05C20 90D05)

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MR0955126 Reviewed Agur, 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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MR0945272 Reviewed Berger, Marc A.; Felzenbaum, Alexander; Fraenkel, Aviezri S. Improvements to the Newman-Znám result for disjoint covering systems. Acta Arith. 50 (1988), no. 1, 1–13. (Reviewer: Š. Znám) 11A07 (11B25)

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MR0945267 Reviewed Berger, 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. Znám) 11B25 (11A07)

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MR0942479 Reviewed Berger, 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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MR0939862 Reviewed Berger, Marc A.; Felzenbaum, Alexander; Fraenkel, Aviezri S. Covers of product sets and the Korec-Znám result. European J. Combin. 9 (1988), no. 2, 131–138. (Reviewer: Ivan Korec) 11B25

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MR0922566 Reviewed Berger, Marc A.; Felzenbaum, Alexander; Fraenkel, Aviezri Remark on the multiplicity of a partition of a group into cosets. Fund. Math. 128 (1987), no. 3, 139–144. (Reviewer: F. Pérez Monasor) 20D60 (20D20)

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MR0899900 Reviewed Fraenkel, Aviezri S.; Goldschmidt, Elisheva PSPACE-hardness of some combinatorial games. J. Combin. Theory Ser. A 46 (1987), no. 1, 21–38. (Reviewer: Andreas Blass) 68Q15 (05C20 90D05 90D42)

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MR0899899 Reviewed Kahane, Joseph; Fraenkel, Aviezri S. k-Welter—a generalization of Welter's game. J. Combin. Theory Ser. A 46 (1987), no. 1, 1–20. (Reviewer: Victor J. Baston) 90D05 (05A99 90D42)

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MR0893463 Reviewed Berger, 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. Znám) 11A07

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MR0891542 Reviewed Berger, M. A.; Felzenbaum, A.; Fraenkel, A. S. Lattice parallelotopes and disjoint covering systems. Discrete Math. 65 (1987), no. 1, 23–46. (Reviewer: Š. Znám) 11B25 (11A07)

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MR0887178 Reviewed Fraenkel, A. S.; Kotzig, A. Partizan octal games: partizan subtraction games. Internat. J. Game Theory 16 (1987), no. 2, 145–154. (Reviewer: G. A. Heuer) 90D05

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MR0880165 Reviewed Apostolico, Alberto; Fraenkel, Aviezri S. Robust transmission of unbounded strings using Fibonacci representations. IEEE Trans. Inform. Theory 33 (1987), no. 2, 238–245. (Reviewer: Andrea Sgarro) 94B45 (94A29)

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MR0875291 Reviewed Berger, M. A.; Felzenbaum, A.; Fraenkel, A. S. A nonanalytic proof of the Newman-Znám result for disjoint covering systems. Combinatorica 6 (1986), no. 3, 235–243. (Reviewer: Š. Znám) 11B25 (11A07 11B83)

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MR0867643 Reviewed Fraenkel, Aviezri S.; Yesha, Yaacov The generalized Sprague-Grundy function and its invariance under certain mappings. J. Combin. Theory Ser. A 43 (1986), no. 2, 165–177. (Reviewer: Harold Reiter) 90D42 (05C20)

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MR0847297 Reviewed Berger, Marc A.; Felzenbaum, Alexander; Fraenkel, Aviezri Necessary condition for the existence of an incongruent covering system with odd moduli. Acta Arith. 45 (1986), no. 4, 375–379. (Reviewer: Š. Znám) 11A07

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MR0846712 Reviewed Berger, Marc A.; Felzenbaum, Alexander; Fraenkel, Aviezri The Herzog-Schönheim conjecture for finite nilpotent groups. Canad. Math. Bull. 29 (1986), no. 3, 329–333. (Reviewer: E. I. Khukhro) 20D60 (20D15)

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MR0843471 Reviewed Berger, Marc A.; Felzenbaum, Alexander; Fraenkel, Aviezri S. Disjoint covering systems of rational Beatty sequences. J. Combin. Theory Ser. A 42 (1986), no. 1, 150–153. (Reviewer: Calvin T. Long) 11B75 (11B83)

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MR0818066 Reviewed Berger, 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 Porubský) 11B25

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MR0824850 Reviewed Berger, Marc A.; Felzenbaum, Alexander; Fraenkel, Aviezri S. Improvements to two results concerning systems of residue sets. Ars Combin. 20 (1985), 69–82. (Reviewer: Š. Znám) 11A07

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MR0815340 Reviewed Fraenkel, 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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MR0815339 Indexed Fraenkel, 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

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MR0789177 Reviewed Fraenkel, Aviezri S.; Nes̆etr̆il, Jaroslav Epidemiography. Pacific J. Math. 118 (1985), no. 2, 369–381. (Reviewer: Klaus Lommatzsch) 90D05 (05C20)

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MR0777556 Reviewed Fraenkel, Aviezri S. Systems of numeration. Amer. Math. Monthly 92 (1985), no. 2, 105–114. (Reviewer: Torleiv Kløve) 11B37

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 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-Znám result. Colloq. Math. 56 (1988), no. 2, 241–249. 

MR0945272 Reviewed Berger, Marc A.; Felzenbaum, Alexander; Fraenkel, Aviezri S. Improvements to the Newman-Znám result for disjoint covering systems. Acta Arith. 50 (1988), no. 1, 1–13. (Reviewer: Š. Znám) 11A07 (11B25)

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MR0945267 Reviewed Berger, 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. Znám) 11B25 (11A07)

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MR0791023 Reviewed Fraenkel, 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)

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MR0744489 Reviewed Boshernitzan, M.; Fraenkel, A. S. A linear algorithm for nonhomogeneous spectra of numbers. J. Algorithms 5 (1984), no. 2, 187–198. (Reviewer: Richard T. Bumby) 11Y55 (68Q40)

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MR0742402 Reviewed Fraenkel, Aviezri S. Wythoff games, continued fractions, cedar trees and Fibonacci searches. Theoret. Comput. Sci. 29 (1984), no. 1-2, 49–73. 68Q20 (05A99 90D05)

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MR0732206 Reviewed Mor, M.; Fraenkel, A. S. Cayley permutations. Discrete Math. 48 (1984), no. 1, 101–112. (Reviewer: M. Livingston) 05A15 (05A05 05C05)

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MR0741904 Reviewed Fraenkel, Aviezri S.; Mor, Moshe Combinatorial compression and partitioning of large dictionaries. Comput. J. 26 (1983), no. 4, 336–343. 68P99 (68R05)

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MR0732312 Reviewed Fraenkel, 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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MR0727659 Reviewed Fraenkel, 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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MR0691047 Reviewed Mor, M.; Fraenkel, A. S. Permutation generation on vector processors. Comput. J. 25 (1982), no. 4, 423–428. 68E99 (05A05 68C05)

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MR0678172 Reviewed Fraenkel, A. S.; Yesha, Y. Theory of annihilation games. I. J. Combin. Theory Ser. B 33 (1982), no. 1, 60–86. (Reviewer: Selim G. Akl) 90D05 (05C20)

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MR0675171 Reviewed Fraenkel, L. E. On the embedding of C1(Ω¯) in C0,α(Ω¯). J. London Math. Soc. (2) 26 (1982), no. 2, 290–298. (Reviewer: J. S. Martins) 46E35

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MR0671176 Reviewed Fraenkel, Aviezri S.; Tassa, Uzi Strategies for compounds of partizan games. Math. Proc. Cambridge Philos. Soc. 92 (1982), no. 2, 193–204. 90D05

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MR0666110 Reviewed Amick, 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)

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MR0660914 Reviewed Fraenkel, Aviezri S. How to beat your Wythoff games' opponent on three fronts. Amer. Math. Monthly 89 (1982), no. 6, 353–361. 90D05

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MR0675689 Reviewed Fraenkel, Aviezri S. Planar kernel and Grundy with d≤3, dout≤2, din≤2 are NP-complete. Discrete Appl. Math. 3 (1981), no. 4, 257–262. 68C25 (05C20)

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MR0635143 Reviewed Fraenkel, Aviezri S.; Lichtenstein, David Computing a perfect strategy for n×n chess requires time exponential in N. Automata, languages and programming (Akko, 1981), pp. 278–293, Lecture Notes in Comput. Sci., 115, Springer, Berlin-New York, 1981. 90D05 (68C25)

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MR0629595 Reviewed Fraenkel, Aviezri S.; Lichtenstein, David Computing a perfect strategy for n×n chess requires time exponential in n. J. Combin. Theory Ser. A 31 (1981), no. 2, 199–214. 68C25 (90D05)

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MR0616779 Reviewed Fraenkel, L. E. A lower bound for electrostatic capacity in the plane. Proc. Roy. Soc. Edinburgh Sect. A 88 (1981), no. 3-4, 267–273. 78A30 (31A15 49G05 52A40)

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MR0613413 Reviewed Boshernitzan, M.; Fraenkel, A. S. Nonhomogeneous spectra of numbers. Discrete Math. 34 (1981), no. 3, 325–327. 10L10

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MR1572333 DML Fraenkel, Aviezri S.; Herda, Hans; News and Letters. Math. Mag. 53 (1980), no. 1, 59–61.

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MR0593528 Reviewed Fraenkel, Aviezri S. From Nim to Go. Ann. Discrete Math. 6 (1980), 137–156. (Reviewer: Harold Reiter) 90D05 (05C20 68C25)

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MR1567093 DML Fraenkel, 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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MR0523586 Reviewed Fraenkel, 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)

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MR0496795 Reviewed Fraenkel, Aviezri S.; Tassa, Uzi; Yesha, Yaacov Three annihilation games. Math. Mag. 51 (1978), no. 1, 13–17. (Reviewer: Stanisław Zdrzałka) 90D99

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MR0464779 Reviewed Attar, 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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MR0429815 Reviewed Fraenkel, Aviezri S. Complementary systems of integers. Amer. Math. Monthly 84 (1977), no. 2, 114–115. (Reviewer: Jau-Shyong Shiue) 10L05 (10A40)

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MR0449726 Reviewed Fraenkel, A. S.; Yesha, Y. Theory of annihilation games. Bull. Amer. Math. Soc. 82 (1976), no. 5, 775–777. (Reviewer: Richard K. Guy) 90D05 (05C20)

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MR0414115 Reviewed Fraenkel, 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

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