Groups of singular alternating sign matrices
Fuente:
arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866917673502244864 |
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| author | O'Brien, Cian Quinlan, Rachel |
| author_facet | O'Brien, Cian Quinlan, Rachel |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_13611 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Groups of singular alternating sign matrices O'Brien, Cian Quinlan, Rachel Rings and Algebras Combinatorics Group Theory 15A30, 15B36, 05B20 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. |
| title | Groups of singular alternating sign matrices |
| topic | Rings and Algebras Combinatorics Group Theory 15A30, 15B36, 05B20 |
| url | https://arxiv.org/abs/2405.13611 |