2011/06/15 by Matthias Lenz, Lenz, Matthias · 1 citation
Computer Science · Mathematics · #05B35 #05C31 #Advanced Combinatorial Mathematics #Combinatorics (math.CO) #Commutative Algebra and Its Applications #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #FOS: Mathematics #Primary: 05A20 #Secondary: 05E45 #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.1106.2944
openalex publication_date 2011/06/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We show that f-vectors of matroid complexes of realisable matroids are log-concave. This was conjectured by Mason in 1972. Our proof uses the recent result by Huh and Katz who showed that the coefficients of the characteristic polynomial of a realisable matroid form a log-concave sequence. We also discuss the relationship between log-concavity of f-vectors and h-vectors of matroids. In the last section we explain the connection between zonotopal algebra and f-vectors and characteristic polynomials of matroids.