Matroids and log-concavity
Combinatorics
2013-06-11 v4 Discrete Mathematics
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.
Keywords
Cite
@article{arxiv.1106.2944,
title = {Matroids and log-concavity},
author = {Matthias Lenz},
journal= {arXiv preprint arXiv:1106.2944},
year = {2013}
}
Comments
9 pages