Vectors of matroids over tracts

h-Vectors of matroids and logarithmic concavity

Article history: Received 11 November 2012 Accepted 4 November 2014 Available online 13 November 2014 Communicated by Ezra Miller MSC: 05B35 52C35

Matroids over a ring

We introduce the notion of a matroid M over a commutative ring R, assigning to every subset of the ground set an R-module according to some axioms. When R is a field, we recover matroids. When R = Z, and when R is a DVR, we get (structures which contain all the data of) quasi-arithmetic matroids, and valuated matroids, respectively. More generally, whenever R is a Dedekind domain, we extend the...

Covering Vectors by Spaces: Regular Matroids

We consider 5the problem of covering a set of vectors of a given finite dimensional linear space (vector space) by a subspace generated by a set of vectors of minimum size. Specifically, we study the Space Cover problem, where we are given a matrix M and a subset of its columns T ; the task is to find a minimum set F of columns of M disjoint with T such that that the linear span of F contains a...

Matroids: h-vectors, Zonotopes, and Lawrence Polytopes

Zeros Of Reliability Polynomials And F-Vectors Of Matroids

For a finite multigraph G, the reliability function of G is the probability RG(q) that if each edge of G is deleted independently with probability q then the remaining edges of G induce a connected spanning subgraph of G; this is a polynomial function of q. In 1992, Brown and Colbourn conjectured that for any connected multigraph G, if q ∈ C is such that RG(q) = 0 then |q| ≤ 1. We verify that t...