Short proof of the ASM theorem avoiding the six-vertex model

DOI10.1016/j.jcta.2016.06.007zbMath1343.05020OpenAlexW2482053609MaRDI QIDQ739388

Ilse Fischer

Publication date: 18 August 2016

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

Full work available at URL: https://doi.org/10.1016/j.jcta.2016.06.007

zbMATH Keywords

exact enumerationalternating sign matricesmonotone triangles

Mathematics Subject Classification ID

Exact enumeration problems, generating functions (05A15) Sign pattern matrices (15B35)

Related Items (12)

The mysterious story of square ice, piles of cubes, and bijections ⋮ Weight-preserving bijections between integer partitions and a class of alternating sign trapezoids ⋮ The relation between alternating sign matrices and descending plane partitions: \(n + 3\) pairs of equivalent statistics ⋮ Weight-preserving bijections between integer partitions and a family of alternating sign trapezoids ⋮ A bijective proof of the ASM theorem. I: The operator formula ⋮ GOE fluctuations for the maximum of the top path in alternating sign matrices ⋮ The first bijective proof of the refined ASM theorem ⋮ Refined enumeration of symmetry classes of alternating sign matrices ⋮ A new determinant for the \(Q\)-enumeration of alternating sign matrices ⋮ Refined enumeration of halved monotone triangles and applications to vertically symmetric alternating sign trapezoids ⋮ Constant term formulas for refined enumerations of Gog and Magog trapezoids ⋮ Enumeration of alternating sign triangles using a constant term approach

Uses Software

• ROBBINS

Cites Work

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