Chow Rings of Vector Space Matroids
Abstract
The Chow ring of a matroid (or more generally, atomic latice) is an invariant whose importance was demonstrated by Adiprasito, Huh and Katz, who used it to resolve the longstanding HeronRotaWelsh conjecture. Here, we make a detailed study of the Chow rings of uniform matroids and of matroids of finite vector spaces. In particular, we express the Hilbert series of such matroids in terms of permutation statistics; in the full rank case, our formula yields the majexc $q$Eulerian polynomials of Shareshian and Wachs. We also provide a formula for the CharneyDavis quantities of such matroids, which can be expressed in terms of either determinants or $q$secant numbers.
 Publication:

arXiv eprints
 Pub Date:
 February 2018
 arXiv:
 arXiv:1802.04241
 Bibcode:
 2018arXiv180204241H
 Keywords:

 Mathematics  Combinatorics