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Finite record sets of
chip-firing games
Kentaro Akasaka, Suguru Ishibashi and Masahiko Yoshinaga |
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Vol. 20 (2023), No. 1, 55–61
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Abstract |
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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. |
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Keywords
chip-firing game, languages
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Mathematical Subject Classification
Primary: 05C57
Secondary: 05C50, 37E25
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Milestones
Received: 6 February 2022
Revised: 28 December 2022
Accepted: 24 January 2023
Published: 11 September 2023
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Authors |
| Kentaro Akasaka | |
| Department of Mathematics Hokkaido University Sapporo 060-0810 Japan |
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| Suguru Ishibashi | |
| Department of Mathematics Hokkaido University Sapporo 060-0810 Japan |
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| Masahiko Yoshinaga | |
| Department of Mathematics Osaka University Toyonaka 560-0043 Japan |
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| © 2023 MSP (Mathematical Sciences Publishers). |
