The Mathematics of Chip-firing is a solid introduction and overview of the growing field of
chip-firing. It offers an appreciation for the richness and diversity of the subject. Chip-firing …

The Tutte polynomial of a graph or a matroid, named after WT Tutte, has the important
universal property that essentially any multiplicative graph or network invariant with a …

Our work, which makes an extensive use of both algebraic and combinatorial techniques, in
particular includes:(i) A characterization of the first half of a pure O-sequence, which yields …

Enumerative combinatorics is about counting. The typical question is to find the number of
objects with a given set of properties. However, enumerative combinatorics is not just about …

We consider the problem of determining mn, the number of matroids on n elements. The
best known lower bound on mn is due to Knuth (1974) who showed that loglog mn is at least …

Basis-exchange properties of sparse paving matroids Page 1 Advances in Applied
Mathematics 50 (2013) 6–15 Contents lists available at SciVerse ScienceDirect Advances in …

In this paper we study the interplay between the operation of circuit-hyperplane relaxation
and the Kazhdan–Lusztig theory of matroids. We obtain a family of polynomials, not …

We prove that the external activity complex Act<(M) of a matroid is shellable. In fact, we show
that every linear extension of Las Vergnas's external/internal order< ext/int on M provides a …

It is shown that the-vectors of Stanley–Reisner rings of three classes of matroids are pure O-
sequences. The classes are (a) matroids that are truncations of matroids, or more generally …

We prove that the Tutte polynomial of a coloopless paving matroid is convex along the
portion of the line x+ y= p lying in the positive quadrant. Every coloopless paving matroid is …