2024/10/30 by Ryuji Inagaki, Tanya Khovanova, Inagaki, Ryota +2 · 2 citations
Biochemistry, Genetics and Molecular Biology · Computer Science · #05A05 #05A15 #05C57 #05C63 #Cellular Automata and Applications #Combinatorics (math.CO) #DNA and Biological Computing #FOS: Mathematics #Interconnection Networks and Systems
paper · pdf · doi:10.48550/arxiv.2410.23265
openalex publication_date 2024/10/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 rooted directed k-ary tree, where we place k^ℓ chips on the root for some positive integer ℓ, and we say a vertex v can fire if it has at least k chips. A vertex fires by dispersing one chip to each out-neighbor. Once every vertex has less than k chips, we reach a stable configuration since no vertex can fire. We determine the exact number and properties of the possible stable configurations of chips in the setting where chips are distinguishable.