This paper surveys some combinatorial aspects of Smith normal form, and more generally,
diagonal form. The discussion includes general algebraic properties and interpretations of …

This is a survey of distance-regular graphs. We present an introduction to distance-regular
graphs for the reader who is unfamiliar with the subject, and then give an overview of some …

We study the interplay between chip-firing games and potential theory on graphs,
characterizing reduced divisors (G-parking functions) on graphs as the solution to an energy …

We determine the distribution of the sandpile group (or Jacobian) of the Erdős-Rényi
random graph $ G (n, q) $ as $ n $ goes to infinity. We prove the distribution converges to a …

Many invertible actions $\tau $ on a set $\mathcal {S} $ of combinatorial objects, along with a
natural statistic $ f $ on $\mathcal {S} $, exhibit the following property which we dub …

We review the status of the two-dimensional Abelian sandpile model as a strong candidate
to provide a lattice realization of logarithmic conformal invariance with a central charge c …

We discuss linear series on tropical curves and their relation to classical algebraic geometry,
describe the main techniques of the subject, and survey some of the recent major …

We study the distribution of the sandpile group of random $ d $-regular graphs. For the
directed model, we prove that it follows the Cohen-Lenstra heuristics, that is, the limiting …

The Abelian sandpile growth model is a diffusion process for configurations of chips placed
on vertices of the integer lattice Z d, in which sites with at least 2 d chips topple, distributing …

The Abelian sandpile process evolves configurations of chips on the integer lattice by
toppling any vertex with at least 4 chips, distributing one of its chips to each of its 4 …