h-Vectors of matroids and logarithmic concavity

2012/01/13 by June Huh, Huh, June · 2 citations
Computer Science · Mathematics · #05B35 #52C35 #Advanced Combinatorial Mathematics #Combinatorics (math.CO) #Commutative Algebra and Its Applications #FOS: Mathematics #Topological and Geometric Data Analysis

paper · pdf · doi:10.48550/arxiv.1201.2915

openalex publication_date 2012/01/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let M be a matroid on E, representable over a field of characteristic zero. We show that h-vectors of the following simplicial complexes are log-concave: 1. The matroid complex of independent subsets of E. 2. The broken circuit complex of M relative to an ordering of E. The first implies a conjecture of Colbourn on the reliability polynomial of a graph, and the second implies a conjecture of Hoggar on the chromatic polynomial of a graph. The proof is based on the geometric formula for the characteristic polynomial of Denham, Garrousian, and Schulze.

Citations

• Matroids and log-concavity

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