Download this article
 Download this article For screen
For printing
Recent Issues
Volume 18
Volume 16
Volume 15
Volume 14
Volume 13
Volume 12
Volume 11
Volume 10
Volume 9
Volume 8
Volume 6+7
Volume 5
Volume 4
Volume 3
Volume 2
Volume 1
The Journal
About the journal
Ethics and policies
Peer-review process
 
Submission guidelines
Submission form
Editorial board
 
Subscriptions
 
ISSN (electronic): 2640-7345
ISSN (print): 2640-7337
Author Index
To Appear
 
Other MSP Journals
Finite record sets of chip-firing games

Kentaro Akasaka, Suguru Ishibashi and Masahiko Yoshinaga

Vol. 20 (2023), No. 1, 55–61
Abstract

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.

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