Séminaire Lotharingien de Combinatoire, 89B.88 (2023), 12 pp.

Hsin-Chieh Liao

Stembridge Codes and Chow Rings Abstract. It is well known that the Eulerian polynomial is the Hilbert series of the cohomology of the permutohedral variety. We answer a question of Stembridge on finding a geometric explanation of the \emph{permutation representation} this cohomology carries. Our explanation involves an S_{n-equivariant bijection between a basis for the Chow ring of the Boolean matroid and codes introduced by Stembridge. There are analogous results for the stellohedral variety. We provide a geometric explanation of the permutation representation that its cohomology carries. This involves the augmented Chow ring of a matroid introduced by Braden, Huh, Matherne, Proudfoot and Wang. Along the way, we also obtain some new results on augmented Chow rings.

Received: November 15, 2022.
Accepted: February 20, 2023.
Final version: April 1, 2023.

The following versions are available:

PDF (211 K)
TeX version}