PlumX Metrics
Embed PlumX Metrics

On the geometry of flag Hilbert-Poincaré series for matroids

Algebraic Combinatorics, ISSN: 2589-5486, Vol: 6, Issue: 3, Page: 623-638
2023
  • 3
    Citations
  • 0
    Usage
  • 0
    Captures
  • 0
    Mentions
  • 0
    Social Media
Metric Options:   Counts1 Year3 Year

Metrics Details

  • Citations
    3

Article Description

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.

Provide Feedback

Have ideas for a new metric? Would you like to see something else here?Let us know