Geodesic
On the geometry of flag Hilbert–Poincaré series for matroids
Kühne, Lukas1 ; Maglione, Joshua1
1 Fakultät für Mathematik, Universität Bielefeld, D-33501 Bielefeld, Germany
Algebraic Combinatorics, Tome 6 (2023) no. 3, pp. 623-638

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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.

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DOI : 10.5802/alco.276
Classification : 05B35, 52C40
Keywords: Coarse flag polynomial, Eulerian polynomials, Igusa zeta functions, oriented matroids

Kühne, Lukas 1 ; Maglione, Joshua 1

1 Fakultät für Mathematik, Universität Bielefeld, D-33501 Bielefeld, Germany
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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     journal = {Algebraic Combinatorics},
     pages = {623--638},
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Kühne, Lukas; Maglione, Joshua. On the geometry of flag Hilbert–Poincaré series for matroids. Algebraic Combinatorics, Tome 6 (2023) no. 3, pp. 623-638. doi: 10.5802/alco.276

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