h-vector inequalities under weak maps

2023/05/24 by Liu, Gaku, Mason, Alexander
#05B35 #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2305.15600

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.

Related

• h-vectors of matroid complexes
• Inequalities for the h-Vectors and Flag h-Vectors of Geometric Lattices
• g-elements of matroid complexes
• h-vectors of small matroid complexes
• Lower bounds for h-vectors of k-CM, independence and broken circuit complexes