On combinatorial algebras generated by three commuting matrices
Fuente:
arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
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| _version_ | 1866918219360501760 |
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| author | Cherny, Ron Quang, Tam An Le Satriano, Matthew |
| author_facet | Cherny, Ron Quang, Tam An Le Satriano, Matthew |
| contents | Motzkin and Taussky (and independently, Gerstenhaber) proved that the unital algebra generated by a pair of commuting $d\times d$ matrices over a field has dimension at most $d$. Since then, it has remained an open problem to determine whether the analogous statement is true for triples of matrices which pairwise commute. We answer this question for combinatorially-motivated classes of such triples. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_22092 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On combinatorial algebras generated by three commuting matrices Cherny, Ron Quang, Tam An Le Satriano, Matthew Commutative Algebra Combinatorics Motzkin and Taussky (and independently, Gerstenhaber) proved that the unital algebra generated by a pair of commuting $d\times d$ matrices over a field has dimension at most $d$. Since then, it has remained an open problem to determine whether the analogous statement is true for triples of matrices which pairwise commute. We answer this question for combinatorially-motivated classes of such triples. |
| title | On combinatorial algebras generated by three commuting matrices |
| topic | Commutative Algebra Combinatorics |
| url | https://arxiv.org/abs/2511.22092 |