Matroids and log-concavity
arXiv:1106.2944
Abstract
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.
9 pages
References in corpus (7)
- Log-concavity, ultra-log-concavity, and a maximum entropy property of discrete compound Poisson measures
- Products of Linear Forms and Tutte Polynomials
- Hierarchical zonotopal spaces
- Hierarchical zonotopal power ideals
- External zonotopal algebra
- Log-concavity of characteristic polynomials and the Bergman fan of matroids
- h-Vectors of matroids and logarithmic concavity
Cited by in corpus (6)
- Hierarchical zonotopal power ideals
- Arithmetic matroids, Tutte polynomial, and toric arrangements
- Log-concavity of characteristic polynomials and the Bergman fan of matroids
- Log-concave poset inequalities
- Toric and tropical compactifications of hyperplane complements
- h-Vectors of matroids and logarithmic concavity