``Proof of the alternating sign matrix conjecture'' ( Elect. J. of Comb. 3(2)(1996),[ special issue in honor of Dominique Foata's 60th birthday], R13)

By Doron Zeilbeger

Even though by now there is a shorter proof, the significance of this paper is still very high. Mainly because the structured way in which it was written, enabling the simultaneous checking by more than eighty five people, who kindly responded to my request for checkers.

But also because the method of proof, I am sure, could be used in many other problems that will come up in the future, especially in statistical mechanics. Moreover, in this paper, I prove a more general result (lemma 1, that should be really called a theorem), that the number of Gog trapezoids equals the number of Magog trapezoids of the same size. The Izergin-Korepin formula, used by Kuperberg to deduce the ASM theorem, is incapable of proving this more general result.

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This paper is accompanied by the Maple package ROBBINS

Added March 16, 1999: Dave Bressoud and Jim Propp wrote a delightful and fascinating account about the proofs of the ASM conjecture and their ramification.

Added June 8, 1999: Dave and Jim's article has just appeared in The June/July 1999 issue of the Notices of the American Mathematical Society.

Added Fall 1999: Read Dave Bressoud's beautiful book about this entitled `Proofs and Confirmations: The Story of the Alterning Sign Matrix Conjecture', published by Amer. Assoc. Math and Camb. Univ. Press.

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