Equivariant Tutte Polynomial
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866918146671116288 |
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| author | Bauer, Mario Doležálek, Matěj Mišinová, Magdaléna Słobodianiuk, Semen Weigert, Julian |
| author_facet | Bauer, Mario Doležálek, Matěj Mišinová, Magdaléna Słobodianiuk, Semen Weigert, Julian |
| contents | We use the equivariant cohomology ring of the permutohedral variety to study matroids and their invariants. Investigating the pushforward of matroid Chern classes defined by A. Berget, C. Eur, H. Spink and D. Tseng to the product space $\mathbb{P}^n \times \mathbb{P}^n$, we establish an equivariant generalization of the Tutte polynomial of a matroid. This was suggested in a survey paper by M.Michałek. We discuss how this polynomial encodes properties of the matroid by looking at special evaluations. We further introduce an equivariant generalization of the reduced characteristic polynomial of a matroid. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_00913 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Equivariant Tutte Polynomial Bauer, Mario Doležálek, Matěj Mišinová, Magdaléna Słobodianiuk, Semen Weigert, Julian Algebraic Geometry Combinatorics 14C15 (Primary) 05E14, 14C17 (Secondary) We use the equivariant cohomology ring of the permutohedral variety to study matroids and their invariants. Investigating the pushforward of matroid Chern classes defined by A. Berget, C. Eur, H. Spink and D. Tseng to the product space $\mathbb{P}^n \times \mathbb{P}^n$, we establish an equivariant generalization of the Tutte polynomial of a matroid. This was suggested in a survey paper by M.Michałek. We discuss how this polynomial encodes properties of the matroid by looking at special evaluations. We further introduce an equivariant generalization of the reduced characteristic polynomial of a matroid. |
| title | Equivariant Tutte Polynomial |
| topic | Algebraic Geometry Combinatorics 14C15 (Primary) 05E14, 14C17 (Secondary) |
| url | https://arxiv.org/abs/2312.00913 |