Alternating sign matrices of finite multiplicative order

O'Brien, Cian and Quinlan, Rachel 2022. Alternating sign matrices of finite multiplicative order. Linear Algebra and its Applications 651 , pp. 332-358. 10.1016/j.laa.2022.06.001

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Abstract

We investigate alternating sign matrices that are not permutation matrices, but have finite order in a general linear group. We classify all such examples of the form , where P is a permutation matrix and T has four non-zero entries, forming a square with entries 1 and −1 in each row and column. We show that the multiplicative orders of these matrices do not always coincide with those of permutation matrices of the same size. We pose the problem of identifying finite subgroups of general linear groups that are generated by alternating sign matrices.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Mathematics
Additional Information:	License information from Publisher: LICENSE 1: URL: http://creativecommons.org/licenses/by/4.0/, Start Date: 2022-06-02
Publisher:	Elsevier
ISSN:	0024-3795
Date of First Compliant Deposit:	11 July 2022
Date of Acceptance:	1 June 2022
Last Modified:	10 May 2023 11:51
URI:	https://orca.cardiff.ac.uk/id/eprint/151238

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