Chip-Firing on Infinite k-ary Trees

2025/01/12 by Agrawal, Dillan, Selena Ge, Jate Greene +18
Computer Science · Mathematics · Physics and Astronomy · #05C57 #05C63 #Cellular Automata and Applications #Combinatorics (math.CO) #FOS: Mathematics #Stochastic processes and statistical mechanics #Theoretical and Computational Physics

paper · pdf · doi:10.48550/arxiv.2501.06675

openalex publication_date 2025/01/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We use an infinite k-ary tree with a self-loop at the root as our underlying graph. We consider a chip-firing process starting with N chips at the root. We describe the stable configurations. We calculate the number of fires for each vertex and the total number of fires. We study a sequence of the number of root fires for a given k as a function of N and study its properties. We do the same for the total number of fires.

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