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Finite record sets of chip-firing games

Kentaro Akasaka, Suguru Ishibashi and Masahiko Yoshinaga

Vol. 20 (2023), No. 1, 55–61

A finite graph with an assignment of nonnegative integers to vertices gives chip-firing games. Chip-firing games determine languages (sets of words) called the record sets of legal games. Björner, Lovász and Shor found several properties that are satisfied by record sets. In this paper, we will find two more properties of record sets. Under the assumption that the record set is finite and the game fires only two vertices, these properties characterize the record sets of graphs.

chip-firing game, languages
Mathematical Subject Classification
Primary: 05C57
Secondary: 05C50, 37E25
Received: 6 February 2022
Revised: 28 December 2022
Accepted: 24 January 2023
Published: 11 September 2023
Kentaro Akasaka
Department of Mathematics
Hokkaido University
Sapporo 060-0810
Suguru Ishibashi
Department of Mathematics
Hokkaido University
Sapporo 060-0810
Masahiko Yoshinaga
Department of Mathematics
Osaka University
Toyonaka 560-0043