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[[FILE:Fraenkel Aviezri 20040503.jpg|border|right|thumb| Aviezri Fraenkel <ref>[https://en.wikipedia.org/wiki/Aviezri_Fraenkel Aviezri Fraenkel from Wikipedia]</ref> ]]
'''Aviezri Siegmund Fraenkel''',<br/>
an Israeli mathematician, computer scientist and pioneer in [https://en.wikipedia.org/wiki/Combinatorial_game_theory combinatorial game theory] and [https://en.wikipedia.org/wiki/Game_complexity game complexity], in particular interested in [https://en.wikipedia.org/wiki/Wythoff%27s_game Wythoff's game] and the game of [https://en.wikipedia.org/wiki/Nim Nim]. He is affiliated with the Department of Computer Science and Applied Mathematics at [https://en.wikipedia.org/wiki/Weizmann_Institute_of_Science Weizmann Institute of Science], [https://en.wikipedia.org/wiki/Rehovot Rehovot]. Fraenkel was member of the team who built the [https://en.wikipedia.org/wiki/WEIZAC WEIZAC], the first computer in [https://en.wikipedia.org/wiki/Israel Israel], and received his Ph.D. in 1961 from [https://en.wikipedia.org/wiki/University_of_California,_Los_Angeles University of California, Los Angeles] on ''Rational Approximations to Algebraic Numbers'' under advisor [[Mathematician#EGStraus|Ernst Gabor Straus]] <ref>[[Aviezri Fraenkel|Aviezri S. Fraenkel]] ('''1961'''). ''Rational Approximations to Algebraic Numbers.'' Dissertation, [https://en.wikipedia.org/wiki/University_of_California,_Los_Angeles University of California, Los Angeles], advisor [[Mathematician#EGStraus|Ernst Gabor Straus]]</ref> <ref>[http://genealogy.math.ndsu.nodak.edu/id.php?id=18990 The Mathematics Genealogy Project - Aviezri Fraenkel]</ref>. Aviezri Fraenkel is combinatorial game Section Editor of the [[ICGA Journal]].
=Selected Publications=
<ref>[http://www.informatik.uni-trier.de/~ley/db/indices/a-tree/f/Fraenkel:Aviezri_S=.html DBLP: Aviezri S. Fraenkel]</ref>
==1960 ...==
* [[Aviezri Fraenkel]] ('''1961'''). ''Rational Approximations to Algebraic Numbers.'' Dissertation, [https://en.wikipedia.org/wiki/University_of_California,_Los_Angeles University of California, Los Angeles], advisor [[Mathematician#EGStraus|Ernst Gabor Straus]]
==1970 ...==
* [[Aviezri Fraenkel]], [[Mathematician#IBorosh|Itzhak Borosh]] ('''1973'''). ''A Generalization of Wythoff's Game''. [http://www.informatik.uni-trier.de/~ley/db/journals/jct/jcta15.html#FraenkelB73 Journal of Combinatorial Theory, Ser. A, Vol. 15, No. 2]
* [[Aviezri Fraenkel]] ('''1974'''). ''Combinatorial games with an annihilation rule'', in Joseph P. La Salle (ed.) [http://www.ams.org/bookstore-getitem/item=PSAPM-20 The Influence of Computing on Mathematics Research and Education], Proc. Symp. Appl. Math.
* [[Aviezri Fraenkel]] ('''1977'''). ''Complementary sets of integers''. Amer. Math. Monthly, 84
* [[Aviezri Fraenkel]], [[Mathematician#MRGarey|Michael R. Garey]], [[Mathematician#DSJohnson|David S. Johnson]], [[Mathematician#TCSchaefer|Thomas J. Schaefer]], [[Mathematician#YYesha|Yaacov Yesha]] ('''1978'''). ''The Complexity of Checkers on an N * N Board''. [http://www.informatik.uni-trier.de/~ley/db/conf/focs/focs78.html#FraenkelGJSY78 FOCS 1978]
==1980 ...==
* [[Aviezri Fraenkel]], [http://www.informatik.uni-trier.de/~ley/db/indices/a-tree/l/Lichtenstein:David.html David Lichtenstein] ('''1981'''). ''[http://link.springer.com/chapter/10.1007/3-540-10843-2_23 Computing a Perfect Strategy for n x n Chess Requires Time Exponential in N]''. [http://www.informatik.uni-trier.de/~ley/db/journals/jct/jcta31.html#FraenkelL81 Journal of Combinatorial Theory, Ser. A, Vol. 31, No. 2]
==1990 ...==
* [[Uri Blass]], [[Aviezri Fraenkel]] ('''1990'''). ''The Sprague-Grundy Function for Wythoff's Game''. [http://www.informatik.uni-trier.de/~ley/db/journals/tcs/tcs75.html Theo. Comp. Sci. 75(3)] <ref>[https://en.wikipedia.org/wiki/Sprague%E2%80%93Grundy_theorem Sprague–Grundy theorem from Wikipedia]</ref><ref>[https://en.wikipedia.org/wiki/Wythoff%27s_game Wythoff's game from Wikipedia]</ref>
* [[Richard K. Guy]], [[John H. Conway]], [[Elwyn Berlekamp]], [[Mathematician#VPless|Vera Pless]], [[Aviezri Fraenkel]], [[Richard J. Nowakowski]] ('''1991'''). ''[https://www.goodreads.com/book/show/5136619-combinatorial-games Combinatorial Games]''. Proceedings of Symposia in Applied Mathematics, No. 43
* [[Aviezri Fraenkel]], [[Dmitri Zusman]] ('''1998'''). ''[http://link.springer.com/chapter/10.1007/3-540-48957-6_13 A New Heap Game]''. [[CG 1998]]
* [[Aviezri Fraenkel]], [[Ofer Rahat]] ('''1998'''). ''[http://link.springer.com/chapter/10.1007/3-540-48957-6_14 Infinite Cyclic Impartial Games]''. [[CG 1998]]
* [[Uri Blass]], [[Aviezri Fraenkel]], [http://www.informatik.uni-trier.de/~ley/db/indices/a-tree/g/Guelman:Romina.html Romina Guelman] ('''1998'''). ''How Far Can Nim in Disguise be Stretched?'' [http://arxiv.org/PS_cache/math/pdf/9809/9809079v1.pdf pdf]
==2000 ...==
* [[Aviezri Fraenkel]] ('''2000'''). ''[http://link.springer.com/chapter/10.1007/3-540-45579-5_13 Virus Versus Mankind]''. [[CG 2000]]
* [[Richard K. Guy]] ('''2001'''). ''Aviezri Fraenkel and Combinatorial Games''. [https://en.wikipedia.org/wiki/Electronic_Journal_of_Combinatorics Electronic Journal of Combinatorics] 8 (2). [http://www.combinatorics.org/Volume_8/PDF/v8i2i2.pdf pdf]
* [[Aviezri Fraenkel]], [[Ofer Rahat]] ('''2002'''). ''[http://link.springer.com/chapter/10.1007/978-3-540-40031-8_14 Complexity of Error-Correcting Codes Derived from Combinatorial Games]''. [[CG 2002]]
* [[Aviezri Fraenkel]] ('''2006'''). ''Nim is Easy, Chess is Hard – But Why??'' [[ICGA Journal#29_4|ICGA Journal, Vol. 29, No. 4]], [http://www.wisdom.weizmann.ac.il/~fraenkel/Papers/ICGA.pdf pdf]
==2010 ...==
* [[Aviezri Fraenkel]] ('''2010'''). ''Complementary Iterated Floor Words and the Flora Game''. SIAM J. on Discrete Math 24, 570--588, [http://www.wisdom.weizmann.ac.il/~fraenkel/Papers/ComplementaryIteratedFlora.pdf pdf]
* [[Aviezri Fraenkel]] ('''2013'''). ''Reflection''. [[ICGA Journal#36_1|ICGA Journal, Vol. 36, No. 1]] » [[Stanislaw Ulam]], [[Monte-Carlo Tree Search]]
=External Links=
* [http://www.wisdom.weizmann.ac.il/%7Efraenkel/ Aviezri Fraenkel's Home Page]
* [https://en.wikipedia.org/wiki/Aviezri_Fraenkel Aviezri Fraenkel from Wikipedia]
* [http://genealogy.math.ndsu.nodak.edu/id.php?id=18990 The Mathematics Genealogy Project - Aviezri Fraenkel]
* [http://www.combinatorics.org/Volume_8/v8i2i1.html Aviezri Fraenkel: A Brief Biography] by Shaula Fraenkel
* [http://www.combinatorics.org/index.html The Electronic Journal of Combinatorics]
=References=
<references />
'''[[People|Up one level]]'''
[[FILE:Fraenkel Aviezri 20040503.jpg|border|right|thumb| Aviezri Fraenkel <ref>[https://en.wikipedia.org/wiki/Aviezri_Fraenkel Aviezri Fraenkel from Wikipedia]</ref> ]]
'''Aviezri Siegmund Fraenkel''',<br/>
an Israeli mathematician, computer scientist and pioneer in [https://en.wikipedia.org/wiki/Combinatorial_game_theory combinatorial game theory] and [https://en.wikipedia.org/wiki/Game_complexity game complexity], in particular interested in [https://en.wikipedia.org/wiki/Wythoff%27s_game Wythoff's game] and the game of [https://en.wikipedia.org/wiki/Nim Nim]. He is affiliated with the Department of Computer Science and Applied Mathematics at [https://en.wikipedia.org/wiki/Weizmann_Institute_of_Science Weizmann Institute of Science], [https://en.wikipedia.org/wiki/Rehovot Rehovot]. Fraenkel was member of the team who built the [https://en.wikipedia.org/wiki/WEIZAC WEIZAC], the first computer in [https://en.wikipedia.org/wiki/Israel Israel], and received his Ph.D. in 1961 from [https://en.wikipedia.org/wiki/University_of_California,_Los_Angeles University of California, Los Angeles] on ''Rational Approximations to Algebraic Numbers'' under advisor [[Mathematician#EGStraus|Ernst Gabor Straus]] <ref>[[Aviezri Fraenkel|Aviezri S. Fraenkel]] ('''1961'''). ''Rational Approximations to Algebraic Numbers.'' Dissertation, [https://en.wikipedia.org/wiki/University_of_California,_Los_Angeles University of California, Los Angeles], advisor [[Mathematician#EGStraus|Ernst Gabor Straus]]</ref> <ref>[http://genealogy.math.ndsu.nodak.edu/id.php?id=18990 The Mathematics Genealogy Project - Aviezri Fraenkel]</ref>. Aviezri Fraenkel is combinatorial game Section Editor of the [[ICGA Journal]].
=Selected Publications=
<ref>[http://www.informatik.uni-trier.de/~ley/db/indices/a-tree/f/Fraenkel:Aviezri_S=.html DBLP: Aviezri S. Fraenkel]</ref>
==1960 ...==
* [[Aviezri Fraenkel]] ('''1961'''). ''Rational Approximations to Algebraic Numbers.'' Dissertation, [https://en.wikipedia.org/wiki/University_of_California,_Los_Angeles University of California, Los Angeles], advisor [[Mathematician#EGStraus|Ernst Gabor Straus]]
==1970 ...==
* [[Aviezri Fraenkel]], [[Mathematician#IBorosh|Itzhak Borosh]] ('''1973'''). ''A Generalization of Wythoff's Game''. [http://www.informatik.uni-trier.de/~ley/db/journals/jct/jcta15.html#FraenkelB73 Journal of Combinatorial Theory, Ser. A, Vol. 15, No. 2]
* [[Aviezri Fraenkel]] ('''1974'''). ''Combinatorial games with an annihilation rule'', in Joseph P. La Salle (ed.) [http://www.ams.org/bookstore-getitem/item=PSAPM-20 The Influence of Computing on Mathematics Research and Education], Proc. Symp. Appl. Math.
* [[Aviezri Fraenkel]] ('''1977'''). ''Complementary sets of integers''. Amer. Math. Monthly, 84
* [[Aviezri Fraenkel]], [[Mathematician#MRGarey|Michael R. Garey]], [[Mathematician#DSJohnson|David S. Johnson]], [[Mathematician#TCSchaefer|Thomas J. Schaefer]], [[Mathematician#YYesha|Yaacov Yesha]] ('''1978'''). ''The Complexity of Checkers on an N * N Board''. [http://www.informatik.uni-trier.de/~ley/db/conf/focs/focs78.html#FraenkelGJSY78 FOCS 1978]
==1980 ...==
* [[Aviezri Fraenkel]], [http://www.informatik.uni-trier.de/~ley/db/indices/a-tree/l/Lichtenstein:David.html David Lichtenstein] ('''1981'''). ''[http://link.springer.com/chapter/10.1007/3-540-10843-2_23 Computing a Perfect Strategy for n x n Chess Requires Time Exponential in N]''. [http://www.informatik.uni-trier.de/~ley/db/journals/jct/jcta31.html#FraenkelL81 Journal of Combinatorial Theory, Ser. A, Vol. 31, No. 2]
==1990 ...==
* [[Uri Blass]], [[Aviezri Fraenkel]] ('''1990'''). ''The Sprague-Grundy Function for Wythoff's Game''. [http://www.informatik.uni-trier.de/~ley/db/journals/tcs/tcs75.html Theo. Comp. Sci. 75(3)] <ref>[https://en.wikipedia.org/wiki/Sprague%E2%80%93Grundy_theorem Sprague–Grundy theorem from Wikipedia]</ref><ref>[https://en.wikipedia.org/wiki/Wythoff%27s_game Wythoff's game from Wikipedia]</ref>
* [[Richard K. Guy]], [[John H. Conway]], [[Elwyn Berlekamp]], [[Mathematician#VPless|Vera Pless]], [[Aviezri Fraenkel]], [[Richard J. Nowakowski]] ('''1991'''). ''[https://www.goodreads.com/book/show/5136619-combinatorial-games Combinatorial Games]''. Proceedings of Symposia in Applied Mathematics, No. 43
* [[Aviezri Fraenkel]], [[Dmitri Zusman]] ('''1998'''). ''[http://link.springer.com/chapter/10.1007/3-540-48957-6_13 A New Heap Game]''. [[CG 1998]]
* [[Aviezri Fraenkel]], [[Ofer Rahat]] ('''1998'''). ''[http://link.springer.com/chapter/10.1007/3-540-48957-6_14 Infinite Cyclic Impartial Games]''. [[CG 1998]]
* [[Uri Blass]], [[Aviezri Fraenkel]], [http://www.informatik.uni-trier.de/~ley/db/indices/a-tree/g/Guelman:Romina.html Romina Guelman] ('''1998'''). ''How Far Can Nim in Disguise be Stretched?'' [http://arxiv.org/PS_cache/math/pdf/9809/9809079v1.pdf pdf]
==2000 ...==
* [[Aviezri Fraenkel]] ('''2000'''). ''[http://link.springer.com/chapter/10.1007/3-540-45579-5_13 Virus Versus Mankind]''. [[CG 2000]]
* [[Richard K. Guy]] ('''2001'''). ''Aviezri Fraenkel and Combinatorial Games''. [https://en.wikipedia.org/wiki/Electronic_Journal_of_Combinatorics Electronic Journal of Combinatorics] 8 (2). [http://www.combinatorics.org/Volume_8/PDF/v8i2i2.pdf pdf]
* [[Aviezri Fraenkel]], [[Ofer Rahat]] ('''2002'''). ''[http://link.springer.com/chapter/10.1007/978-3-540-40031-8_14 Complexity of Error-Correcting Codes Derived from Combinatorial Games]''. [[CG 2002]]
* [[Aviezri Fraenkel]] ('''2006'''). ''Nim is Easy, Chess is Hard – But Why??'' [[ICGA Journal#29_4|ICGA Journal, Vol. 29, No. 4]], [http://www.wisdom.weizmann.ac.il/~fraenkel/Papers/ICGA.pdf pdf]
==2010 ...==
* [[Aviezri Fraenkel]] ('''2010'''). ''Complementary Iterated Floor Words and the Flora Game''. SIAM J. on Discrete Math 24, 570--588, [http://www.wisdom.weizmann.ac.il/~fraenkel/Papers/ComplementaryIteratedFlora.pdf pdf]
* [[Aviezri Fraenkel]] ('''2013'''). ''Reflection''. [[ICGA Journal#36_1|ICGA Journal, Vol. 36, No. 1]] » [[Stanislaw Ulam]], [[Monte-Carlo Tree Search]]
=External Links=
* [http://www.wisdom.weizmann.ac.il/%7Efraenkel/ Aviezri Fraenkel's Home Page]
* [https://en.wikipedia.org/wiki/Aviezri_Fraenkel Aviezri Fraenkel from Wikipedia]
* [http://genealogy.math.ndsu.nodak.edu/id.php?id=18990 The Mathematics Genealogy Project - Aviezri Fraenkel]
* [http://www.combinatorics.org/Volume_8/v8i2i1.html Aviezri Fraenkel: A Brief Biography] by Shaula Fraenkel
* [http://www.combinatorics.org/index.html The Electronic Journal of Combinatorics]
=References=
<references />
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