Straightening laws for Chow rings of matroids
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866916637080289280 |
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| author | Larson, Matt |
| author_facet | Larson, Matt |
| contents | We give elementary and non-inductive proofs of three fundamental theorems about Chow rings of matroids: the standard monomial basis, Poincare duality, and the dragon-Hall-Rado formula. Our approach, which also works for augmented Chow rings of matroids, is based on a straightening law. This approach also gives a decomposition of the Chow ring of a matroid into pieces indexed by flats. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_03444 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Straightening laws for Chow rings of matroids Larson, Matt Combinatorics Commutative Algebra 05B35, 13H10 We give elementary and non-inductive proofs of three fundamental theorems about Chow rings of matroids: the standard monomial basis, Poincare duality, and the dragon-Hall-Rado formula. Our approach, which also works for augmented Chow rings of matroids, is based on a straightening law. This approach also gives a decomposition of the Chow ring of a matroid into pieces indexed by flats. |
| title | Straightening laws for Chow rings of matroids |
| topic | Combinatorics Commutative Algebra 05B35, 13H10 |
| url | https://arxiv.org/abs/2402.03444 |