2020/10/29 by Patrick Liscio, Liscio, Patrick
Computer Science · Mathematics · #05C99 #06D99 #Combinatorics (math.CO) #Computability, Logic, AI Algorithms #FOS: Mathematics #Mathematical Dynamics and Fractals #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.2010.15650
openalex publication_date 2020/10/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.