Matthias Lenz
Published 2011-06-15, updated 2013-06-10Version 4
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.
A categorification for the characteristic polynomial of matroids
The $α$-representation for the characteristic function of a matroid
Matroid variant of Matiyasevich formula and its application
![QR code for arXiv:1106.2944 [math.CO]](http://oss.arxitics.com/images/favicon.svg)