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| Main Author: | |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2406.18932 |
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| _version_ | 1866909858071052288 |
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| author | Stump, Christian |
| author_facet | Stump, Christian |
| contents | We show that Chow polynomials and augmented Chow polynomials of matroids, and more generally of finite graded posets admitting R-labelings, are obtained as evaluations of their Poincaré-extended ab-indices. This implies in particular explicit combinatorial $γ$-positive expansions for both, providing the first proof of the $γ$-positivity not relying on the Kähler package for the Chow ring. We then evaluate this expansion to obtain an explicit closed formula for the braid arrangement. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_18932 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Chow and augmented Chow polynomials as evaluations of Poincaré-extended ab-indices Stump, Christian Combinatorics We show that Chow polynomials and augmented Chow polynomials of matroids, and more generally of finite graded posets admitting R-labelings, are obtained as evaluations of their Poincaré-extended ab-indices. This implies in particular explicit combinatorial $γ$-positive expansions for both, providing the first proof of the $γ$-positivity not relying on the Kähler package for the Chow ring. We then evaluate this expansion to obtain an explicit closed formula for the braid arrangement. |
| title | Chow and augmented Chow polynomials as evaluations of Poincaré-extended ab-indices |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2406.18932 |