Refined enumeration of symmetry classes of alternating sign matrices

被引：2

作者：

Fischer, Ilse ^{[1
]}

Saikia, Manjil P. ^{[1
,2
]}

机构：

[1] Univ Wien, Fak Math, Oskar Morgenstern Pl 1, A-1090 Vienna, Austria

[2] Cardiff Univ, Sch Math, Cardiff CF24 4AG, Wales

来源：

JOURNAL OF COMBINATORIAL THEORY SERIES A | 2021年 / 178卷

基金：

奥地利科学基金会;

关键词：

Alternating sign matrices; Six-vertex model; Symmetry classes of alternating sign matrices; Lozenge tilings of hexagons; Non-intersecting lattice paths; Symplectic group characters; FORMULA; DETERMINANT; CHARACTERS; PROOF;

D O I：

10.1016/j.jcta.2020.105350

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove refined enumeration results on several symmetry classes as well as related classes of alternating sign matrices with respect to classical boundary statistics, using the six-vertex model of statistical physics. More precisely, we study vertically symmetric, vertically and horizontally symmetric, vertically and horizontally perverse, off-diagonally and off-antidiagonally symmetric, vertically and off-diagonally symmetric, quarter turn symmetric as well as quasi quarter turn symmetric alternating sign matrices. Our results prove conjectures of Fischer, Duchon and Robbins. (C) 2020 Elsevier Inc. All rights reserved.

引用

页数：51

共 35 条

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