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arXiv · 2405.13611

Groups of singular alternating sign matrices

Cian O'Brien·Rachel Quinlan
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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.

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Cian O'Brien, Rachel Quinlan. 2024-05-22. Groups of singular alternating sign matrices. https://arxiv.org/abs/2405.13611

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