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 …

Ehrhart discovered that the function that counts the number of lattice points in dilations of an
integral polytope is a polynomial. We call the coefficients of this polynomial Ehrhart …

Given a semisimple element in the loop Lie algebra of a reductive group, we construct a
quasi-coherent sheaf on a partial resolution of the trigonometric commuting variety of the …

Jim Propp recently proposed a labeled version of chip-firing on a line and conjectured that
this process is confluent from some initial configurations. This was proved by Hopkins …

Abstract In 2016, Hopkins, McConville, and Propp proved that labeled chip-firing on a line
always leaves the chips in sorted order provided that the initial number of chips is even. We …

In earlier work in collaboration with Pavel Galashin and Thomas McConville we introduced a
version of chip-firing for root systems. Our investigation of root system chip-firing led us to …

Recall that an excedance of a permutation $\pi $ is any position $ i $ such that $\pi_i> i $.
Inspired by the work of Hopkins, McConville and Propp (Elec. J. Comb., 2017) on sorting …

We consider a discrete non-deterministic flow-firing process for rerouting flow on the edges
of a planar complex. The process is an instance of higher-dimensional chip-firing. In the flow …

The study of toppling on permutations with an extra labeled chip was initiated by the first
author with D. Hathcock and P. Tetali (arXiv: 2010.11236), where the extra chip was added …

We analyze the poset of moves in chip-firing, as defined by Klivans and Liscio. Answering a
question of Propp, we show that the move poset forms the join-irreducibles of the poset of …