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 …

An explicit combinatorial minimal free resolution of an arbitrary monomial ideal $ I $ in a
polynomial ring in $ n $ variables over a field of characteristic $0 $ is defined canonically …

Much information about a graph can be obtained by studying its spanning trees. On the
other hand, a graph can be regarded as a 1-dimensional cell complex, raising the question …

Using ideas from algebraic topology and statistical mechanics, we generalize Kirchhoff's
network and matrix-tree theorems to finite CW complexes of arbitrary dimension. As an …

For a graph G, the generating function of rooted forests, counted by the number of connected
components, can be expressed in terms of the eigenvalues of the graph Laplacian. We …

We initiate the study of group actions on (possibly infinite) semimatroids and geometric
semilattices. To every such action is naturally associated an orbit-counting function, a two …

We characterize the classical Boltzmann distribution as the unique solution to a
combinatorial Hodge theory problem in homological degree zero on a finite graph. By …

We deduce a structurally inductive description of the determinantal probability measure
associated with Kalai's celebrated enumeration result for higher-dimensional spanning trees …

We study linear equations in combinatorial Laplacians of $ k $-dimensional simplicial
complexes ($ k $-complexes), a natural generalization of graph Laplacians. Combinatorial …

We study quasipolynomials enumerating proper colorings, nowhere-zero tensions, and
nowhere-zero flows in an arbitrary CW-complex X, generalizing the chromatic, tension and …