Report
On the geometry of flag Hilbert-Poincar\'e series for matroids
| العنوان: | On the geometry of flag Hilbert-Poincar\'e series for matroids |
|---|---|
| المؤلفون: | Kühne, Lukas, Maglione, Joshua |
| سنة النشر: | 2021 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Combinatorics, Mathematics - Metric Geometry, 05B35, 52C40 |
| الوصف: | We extend the definition of coarse flag Hilbert--Poincar\'e 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. Comment: To appear in Algebraic Combinatorics. 16 pages |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2111.05636 |
| رقم الانضمام: | edsarx.2111.05636 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |