In 1977 Stanley conjectured that the h-vector of a matroid independence complex is a pure
O-sequence. In this paper we use lexicographic shellability for matroids to motivate a new …

We introduce the notion of a quasi-matroidal class of ordered simplicial complexes: an
approximation to the idea of a matroid cryptomorphism in the landscape of ordered …

A well-known conjecture of Stanley is that the h-vector of any matroid is a pure O-sequence.
There have been numerous papers with partial progress on this conjecture, but it is still wide …

A well-known conjecture of Richard Stanley posits that the $ h $-vector of the independence
complex of a matroid is a pure ${\mathcal O} $-sequence. The conjecture has been …

The main objects of study in this thesis are matroids. In particular we are interested in three
particular classes matroids: regular matroids, arithmetic matroids, and internally perfect …

In 1977 Stanley proved that the $ h $-vector of a matroid is an $\mathcal {O} $-sequence and
conjectured that it is a pure $\mathcal {O} $-sequence. In the subsequent years the validity of …

A well-known conjecture of Stanley is that the h-vector of a matroid is a pure O-sequence.
There have been numerous papers with partial progress on this conjecture, but it is still wide …

We introduce the notion of a quasi-matroidal class of ordered simplicial complexes: an
approximation to the idea of a matroid cryptomorphism in the landscape of ordered …

Motivated by a question of Duval and Reiner about higher Laplacians of simplicial
complexes, we describe various relaxations of the defining axioms of matroid theory to …

To a vector configuration one can associate a polynomial ideal generated by powers of
linear forms, known as a power ideal, which exhibits many combinatorial features of the …