A doubly-refined enumeration of alternating sign matrices and descending plane partitions

DOI10.1016/j.jcta.2012.09.004zbMath1256.05031arXiv1202.1520OpenAlexW2072468773MaRDI QIDQ1930141

Roger E. Behrend, Philippe Di Francesco, Paul Zinn-Justin

Publication date: 10 January 2013

Published in: Journal of Combinatorial Theory. Series A (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1202.1520

zbMATH Keywords

Jacobi identitynonintersecting lattice pathsalternating sign matricesdescending plane partitionssix-vertex model with domain-wall boundary conditionsdesnanot

Mathematics Subject Classification ID

Combinatorial aspects of matrices (incidence, Hadamard, etc.) (05B20) Determinants, permanents, traces, other special matrix functions (15A15) Matrices of integers (15B36)

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The mysterious story of square ice, piles of cubes, and bijections ⋮ Extreme diagonally and antidiagonally symmetric alternating sign matrices of odd order ⋮ Twenty-vertex model with domain wall boundaries and domino tilings ⋮ Weight-preserving bijections between integer partitions and a class of alternating sign trapezoids ⋮ Sign matrix polytopes from Young tableaux ⋮ The relation between alternating sign matrices and descending plane partitions: \(n + 3\) pairs of equivalent statistics ⋮ A bijective proof of the ASM theorem. I: The operator formula ⋮ The first bijective proof of the refined ASM theorem ⋮ Multiply-refined enumeration of alternating sign matrices ⋮ Arctic curves of the twenty-vertex model with domain wall boundaries ⋮ A statistics-respecting bijection between permutation matrices and descending plane partitions without special parts ⋮ Enumeration of alternating sign triangles using a constant term approach

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