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Patrick Liscio

Publications and source records attributed to Patrick Liscio.

2 recordsLinked to original sources
arXiv2020

Lattices in Chip-Firing

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.

math.CO↗
arXiv2020

Confluence in Labeled Chip-Firing

In 2016, Hopkins, McConville, and Propp proved that labeled chip-firing on a line always leaves the chips in sorted order if the number of chips is even. We present a novel proof of this result. We then apply our methods to resolve a number of related conjectures concerning the confluence of labeled chip-firing systems.

math.CO↗