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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2601.11246 |
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| _version_ | 1866918292460929024 |
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| author | Fife, Tara Mannino, Eline Rincón, Felipe |
| author_facet | Fife, Tara Mannino, Eline Rincón, Felipe |
| contents | We introduce the rank-nullity ring of a matroid $M$, which is a subring of the Chow ring of the permutahedral toric variety. This subring contains the tautological Chern classes of $M$, a fact we deduce from a highly symmetric formula for these classes. When the matroid $M$ is a uniform matroid, the rank-nullity ring coincides with the subring of $S_n$-invariants of the Chow ring of the permutahedral toric variety. In this case, we compute its Hilbert function explicitly and provide a Gröbner basis for the ideal of relations among its generators. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_11246 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The rank-nullity ring of a matroid Fife, Tara Mannino, Eline Rincón, Felipe Combinatorics Commutative Algebra Algebraic Geometry 52B40, 14C15, 14C17 We introduce the rank-nullity ring of a matroid $M$, which is a subring of the Chow ring of the permutahedral toric variety. This subring contains the tautological Chern classes of $M$, a fact we deduce from a highly symmetric formula for these classes. When the matroid $M$ is a uniform matroid, the rank-nullity ring coincides with the subring of $S_n$-invariants of the Chow ring of the permutahedral toric variety. In this case, we compute its Hilbert function explicitly and provide a Gröbner basis for the ideal of relations among its generators. |
| title | The rank-nullity ring of a matroid |
| topic | Combinatorics Commutative Algebra Algebraic Geometry 52B40, 14C15, 14C17 |
| url | https://arxiv.org/abs/2601.11246 |