Categorical valuative invariants of polyhedra and matroids
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866916448267403264 |
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| author | Elias, Ben Miyata, Dane Proudfoot, Nicholas Vecchi, Lorenzo |
| author_facet | Elias, Ben Miyata, Dane Proudfoot, Nicholas Vecchi, Lorenzo |
| contents | We introduce the notion of a categorical valuative invariant of polyhedra or matroids, in which alternating sums of numerical invariants are replaced by split exact sequences in an additive category. We provide categorical lifts of a number of valuative invariants of matroids, including the Poincare polynomial, the Chow and augmented Chow polynomials, and certain two-variable extensions of the Kazhdan--Lusztig polynomial and Z-polynomial. These lifts allow us to perform calculations equivariantly with respect to automorphism groups of matroids. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_06869 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Categorical valuative invariants of polyhedra and matroids Elias, Ben Miyata, Dane Proudfoot, Nicholas Vecchi, Lorenzo Combinatorics 05B35, 52B45 We introduce the notion of a categorical valuative invariant of polyhedra or matroids, in which alternating sums of numerical invariants are replaced by split exact sequences in an additive category. We provide categorical lifts of a number of valuative invariants of matroids, including the Poincare polynomial, the Chow and augmented Chow polynomials, and certain two-variable extensions of the Kazhdan--Lusztig polynomial and Z-polynomial. These lifts allow us to perform calculations equivariantly with respect to automorphism groups of matroids. |
| title | Categorical valuative invariants of polyhedra and matroids |
| topic | Combinatorics 05B35, 52B45 |
| url | https://arxiv.org/abs/2401.06869 |