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 …

Jim Propp recently introduced a variant of chip-firing on a line where the chips are given
distinct integer labels. Hopkins, McConville, and Propp showed that this process is confluent …

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 …

In this paper we define a variant of the Ising model in which spins are replaced with
permutations. The energy between two spins is a function of the relative disorder of one …

Chip-firing is a combinatorial game played on a graph in which we place and disperse chips
on vertices until a stable state is reached. We study a chip-firing variant played on an infinite …