Year: 2025
Type: article
Abstract: We study the behavior of h -vectors associated to matroid complexes under weak maps, or inclusions of matroid polytopes. Specifically, we show that the h -vector of the order complex of the lattice of flats of a matroid is component-wise non-increasing under a weak map. This result extends to the flag h -vector. We note that the analogous result also holds for independence complexes and rank-preserving weak maps.
Source: Algebraic Combinatorics
DOI: 10.5802/alco.409
Authors: Gaku Liu, Alexander Mason
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4409772136