Lattices in Chip-Firing
Combinatorics
2020-10-30 v1
Abstract
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 configurations. The proof involves a graph augmentation and an analysis of configurations in which only one firing move is available. We then use this framework to analyze the problem of chip-firing on a line, where the move poset is relevant to the problem of labeled chip-firing.
Cite
@article{arxiv.2010.15650,
title = {Lattices in Chip-Firing},
author = {Patrick Liscio},
journal= {arXiv preprint arXiv:2010.15650},
year = {2020}
}
Comments
11 pages, 7 figures