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.
.dvi version (for previewing)
This paper is accompanied by the Maple package ROBBINS
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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