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Refined enumeration of symmetry classes of alternating sign matrices

Fischer, Ilse and Saikia, Manjil 2021. Refined enumeration of symmetry classes of alternating sign matrices. Journal of Combinatorial Theory, Series A 178 , 105350. 10.1016/j.jcta.2020.105350
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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.

Item Type: Article
Date Type: Publication
Status: Published
Schools: Mathematics
Subjects: Q Science > QA Mathematics
Publisher: Elsevier
ISSN: 0097-3165
Funders: Austrian Science Fund FWF
Date of First Compliant Deposit: 11 November 2020
Date of Acceptance: 5 October 2020
Last Modified: 24 Nov 2020 18:11

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