A convex ear decomposition of the augmented Bergman complex of a matroid
Abstract
In recent work of Braden, Huh, Matherne, Proudfoot and Wang, a class of simplicial complexes associated to matroids, called augmented Bergman complexes, was introduced. The present article concerns the face enumeration of these complexes. We prove that the augmented Bergman complex of any matroid admits a convex ear decomposition and deduce that augmented Bergman complexes are doubly Cohen–Macaulay and that they have top-heavy $h$-vectors. We provide some formulas for computing the $h$-polynomials of these complexes and exhibit examples which show that, in general, they are neither log-concave nor unimodal.
Fields of Study & Subjects
Geometry and complex manifolds
Advanced Combinatorial Mathematics
Advanced Topics in Algebra
Publication details
- Journal / source
- Arkiv för matematik
- Publisher
- International Press of Boston
- Volume
- 64
- Issue
- 1
- Pages
- 1–17
- Publication date
- 1 January 2026
- Language
- EN