Groups of singular alternating sign matrices
Rings and Algebras
2024-05-24 v1 Combinatorics
Group Theory
Abstract
We investigate multiplicative groups consisting entirely of singular alternating sign matrices (ASMs), and present several constructions of such groups. It is shown that every finite group is isomorphic to a group of singular ASMs, with a singular idempotent ASM as its identity element. The relationship between the size, the rank, and the possible multiplicative orders of singular ASMs is explored.
Cite
@article{arxiv.2405.13611,
title = {Groups of singular alternating sign matrices},
author = {Cian O'Brien and Rachel Quinlan},
journal= {arXiv preprint arXiv:2405.13611},
year = {2024}
}