Small Matrices with Small Inverses: Unimodular Zerofree Cases
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866914559223136256 |
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| author | Finch, Steven |
| author_facet | Finch, Steven |
| contents | We consider unimodular matrices $M$ such that neither $M$ nor $M^{-1}$ contain zero entries. Matrices typically exhibit a trade-off: small $M$ imply large $M^{-1}$. We investigate rare cases where both remain small, classify these matrices up to symmetry, and discuss aspects of this balanced setting. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_03691 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Small Matrices with Small Inverses: Unimodular Zerofree Cases Finch, Steven Combinatorics Discrete Mathematics Number Theory 15B36 (Primary), 11C20, 05B20, 15A15, 15A21 (Secondary) We consider unimodular matrices $M$ such that neither $M$ nor $M^{-1}$ contain zero entries. Matrices typically exhibit a trade-off: small $M$ imply large $M^{-1}$. We investigate rare cases where both remain small, classify these matrices up to symmetry, and discuss aspects of this balanced setting. |
| title | Small Matrices with Small Inverses: Unimodular Zerofree Cases |
| topic | Combinatorics Discrete Mathematics Number Theory 15B36 (Primary), 11C20, 05B20, 15A15, 15A21 (Secondary) |
| url | https://arxiv.org/abs/2605.03691 |