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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Abstract

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:	20 Nov 2024 22:45
URI:	https://orca.cardiff.ac.uk/id/eprint/136245

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