Companion matrices, permutations and lattice ideals
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Acceso en línea: | |
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| _version_ | 1866917070325678080 |
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| author | Udo, Nsibiet E. Adeyemo, Praise |
| author_facet | Udo, Nsibiet E. Adeyemo, Praise |
| contents | This paper investigates a novel connection between reductions of companion matrices associated with a symmetric family of certain binomial ideals in the coordinate ring of affine n-space and permutation matrices. Specifically, for fixed monomial orders, we observe that the reduced companion matrices yield permutation matrices satisfying group-theoretic relations. We explore the implications of these reductions, their connections to lattice ideals, and characterize the groups generated by these transformations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_06555 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Companion matrices, permutations and lattice ideals Udo, Nsibiet E. Adeyemo, Praise Commutative Algebra Algebraic Geometry Group Theory Representation Theory 13A15, 06B10 (Primary) 20K01, 20D45, 20F28 (Secondary) This paper investigates a novel connection between reductions of companion matrices associated with a symmetric family of certain binomial ideals in the coordinate ring of affine n-space and permutation matrices. Specifically, for fixed monomial orders, we observe that the reduced companion matrices yield permutation matrices satisfying group-theoretic relations. We explore the implications of these reductions, their connections to lattice ideals, and characterize the groups generated by these transformations. |
| title | Companion matrices, permutations and lattice ideals |
| topic | Commutative Algebra Algebraic Geometry Group Theory Representation Theory 13A15, 06B10 (Primary) 20K01, 20D45, 20F28 (Secondary) |
| url | https://arxiv.org/abs/2511.06555 |