# Aviezri Fraenkel

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**Home * People * Aviezri Fraenkel**

**Aviezri Siegmund Fraenkel**,

an Israeli mathematician, computer scientist and pioneer in combinatorial game theory and game complexity, in particular interested in Wythoff's game and the game of Nim. He is affiliated with the Department of Computer Science and Applied Mathematics at Weizmann Institute of Science, Rehovot. Fraenkel was member of the team who built the WEIZAC, the first computer in Israel, and received his Ph.D. in 1961 from University of California, Los Angeles on *Rational Approximations to Algebraic Numbers* under advisor Ernst Gabor Straus ^{[2]} ^{[3]}. Aviezri Fraenkel is combinatorial game Section Editor of the ICGA Journal.

## Contents

# Selected Publications

^{[4]}

## 1960 ...

- Aviezri Fraenkel (
**1961**).*Rational Approximations to Algebraic Numbers.*Dissertation, University of California, Los Angeles, advisor Ernst Gabor Straus

## 1970 ...

- Aviezri Fraenkel, Itzhak Borosh (
**1973**).*A Generalization of Wythoff's Game*. 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.) 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, Michael R. Garey, David S. Johnson, Thomas J. Schaefer, Yaacov Yesha (
**1978**).*The Complexity of Checkers on an N * N Board*. FOCS 1978

## 1980 ...

- Aviezri Fraenkel, David Lichtenstein (
**1981**).*Computing a Perfect Strategy for n x n Chess Requires Time Exponential in N*. Journal of Combinatorial Theory, Ser. A, Vol. 31, No. 2

## 1990 ...

- Uri Blass, Aviezri Fraenkel (
**1990**).*The Sprague-Grundy Function for Wythoff's Game*. Theoretical Computer Science, Vol. 75, No. 3^{[5]}^{[6]} - Richard K. Guy, John H. Conway, Elwyn Berlekamp, Vera Pless, Aviezri Fraenkel, Richard J. Nowakowski (
**1991**).*Combinatorial Games*. Proceedings of Symposia in Applied Mathematics, No. 43 - Aviezri Fraenkel, Dmitri Zusman (
**1998**).*A New Heap Game*. CG 1998 - Aviezri Fraenkel, Ofer Rahat (
**1998**).*Infinite Cyclic Impartial Games*. CG 1998 - Uri Blass, Aviezri Fraenkel, Romina Guelman (
**1998**).*How Far Can Nim in Disguise be Stretched?*Journal of Combinatorial Theory, Series A, Vol. 84, arXiv:math/9809079

## 2000 ...

- Aviezri Fraenkel (
**2000**).*Virus Versus Mankind*. CG 2000 - Richard K. Guy (
**2001**).*Aviezri Fraenkel and Combinatorial Games*. Electronic Journal of Combinatorics 8 (2). pdf - Aviezri Fraenkel, Ofer Rahat (
**2002**).*Complexity of Error-Correcting Codes Derived from Combinatorial Games*. CG 2002 - Aviezri Fraenkel (
**2006**).*Nim is Easy, Chess is Hard – But Why??*ICGA Journal, Vol. 29, No. 4, pdf

## 2010 ...

- Aviezri Fraenkel (
**2010**).*Complementary Iterated Floor Words and the Flora Game*. SIAM J. on Discrete Math 24, 570--588, pdf - Aviezri Fraenkel (
**2013**).*Reflection*. ICGA Journal, Vol. 36, No. 1 » Stanislaw Ulam, Monte-Carlo Tree Search

# External Links

- Aviezri Fraenkel's Home Page
- Aviezri Fraenkel from Wikipedia
- The Mathematics Genealogy Project - Aviezri Fraenkel
- Aviezri Fraenkel: A Brief Biography by Shaula Fraenkel
- The Electronic Journal of Combinatorics

# References

- ↑ A 2004 photo of Aviezri Fraenkel by photographer Douglas Wertheimer, Aviezri Fraenkel from Wikipedia
- ↑ Aviezri S. Fraenkel (
**1961**).*Rational Approximations to Algebraic Numbers.*Dissertation, University of California, Los Angeles, advisor Ernst Gabor Straus - ↑ The Mathematics Genealogy Project - Aviezri Fraenkel
- ↑ DBLP: Aviezri S. Fraenkel
- ↑ Sprague–Grundy theorem from Wikipedia
- ↑ Wythoff's game from Wikipedia