On the geometry of flag Hilbert-Poincaré series for matroids
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arXiv
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| Format: | Preprint |
| Published: |
2021
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| _version_ | 1866910955870355456 |
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| author | Kühne, Lukas Maglione, Joshua |
| author_facet | Kühne, Lukas Maglione, Joshua |
| contents | We extend the definition of coarse flag Hilbert--Poincaré series to matroids; these series arise in the context of local Igusa zeta functions associated to hyperplane arrangements. We study these series in the case of oriented matroids by applying geometric and combinatorial tools related to their topes. In this case, we prove that the numerators of these series are coefficient-wise bounded below by the Eulerian polynomial and equality holds if and only if all topes are simplicial. Moreover this yields a sufficient criterion for non-orientability of matroids of arbitrary rank. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2111_05636 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | On the geometry of flag Hilbert-Poincaré series for matroids Kühne, Lukas Maglione, Joshua Combinatorics Metric Geometry 05B35, 52C40 We extend the definition of coarse flag Hilbert--Poincaré series to matroids; these series arise in the context of local Igusa zeta functions associated to hyperplane arrangements. We study these series in the case of oriented matroids by applying geometric and combinatorial tools related to their topes. In this case, we prove that the numerators of these series are coefficient-wise bounded below by the Eulerian polynomial and equality holds if and only if all topes are simplicial. Moreover this yields a sufficient criterion for non-orientability of matroids of arbitrary rank. |
| title | On the geometry of flag Hilbert-Poincaré series for matroids |
| topic | Combinatorics Metric Geometry 05B35, 52C40 |
| url | https://arxiv.org/abs/2111.05636 |