This page lists some of my preprints, recent reprints, and indicates
how to access my Games Bibliography. Also my special favorite, the
Responsa Project, is
mentioned briefly.
E. Duchene, A.S. Fraenkel, V. Gurvich, N.B. Ho, C. Kimberling and U. Larsson, Wythoff Wisdom, to appear in Games of No Chance 5. Preprint.
A.S. Fraenkel and M. Rigo Games derived from a generalized Thue-Morse word, Preprint.
L. Goldberg and A.S. Fraenkel, Take-away games on Beatty's Theorem and the notion of k-invariance, to appear in Games of No Chance 5.
L. Goldberg and A.S. Fraenkel, Extensions of Wythoff's game, Preprint.
A.S. Fraenkel, Complementary balanced words over an arbitrary finite alphabet.
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 .
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 translations 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,
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,
Combinatorial game theory foundations applied to digraph kernels
, Electronic J. of
Combinatorics 4(2) (1997) R10, 17pp. (Wilf Festschrift).
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
.
URL for this homepage is:
http://www.wisdom.weizmann.ac.il/~fraenkel
Return for additional wisdom
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 .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.The Good Countries and the Good People Therein
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."Personal Data
