Another proof of the alternating sign matrix conjecture

1997/11/29 by Greg Kuperberg · 3 citations
Mathematics · #math.CO

paper · pdf

published as Internat. Math. Res. Notices, 1996(3):139-150, 1996 · 10 pages

arxiv created 1997/11/29 · arxiv updated 2009/11/30

Abstract

Robbins conjectured, and Zeilberger recently proved, that there are 1!4!7!...(3n-2)!/n!/(n+1)!/.../(2n-1)! alternating sign matrices of order n. We give a new proof of this result using an analysis of the six-vertex state model (also called square ice) based on the Yang-Baxter equation.

Cited by

• Bicolored bosonic solvable lattice models
• Frozen-corner enumeration of Alternating Sign Matrices
• A short combinatorial proof of Di Francesco's conjecture on Aztec triangles

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• A new proof of the refined alternating sign matrix theorem
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