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Characterization of simple edge-firing games

✍ Scribed by Oliver Pretzel

Book ID: 104136808
Publisher: Elsevier Science
Year: 2002
Tongue: English
Weight: 31 KB
Volume: 84
Category: Article
ISSN: 0020-0190
DOI: 10.1016/s0020-0190(02)00311-3

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✦ Synopsis

In a recent publication, Latapy and Magnien [Inform. Process. Lett. 83 (2002) 125-128] show how every distributive lattice can be represented as the set of configurations of a simple edge firing game (EFG). This is a converse of the result of Propp [Preprint, 1993] that shows that the set of configurations of an EFG forms a distributive lattice. Using this result and then the result of Latapy and Magnien gives an algorithm for converting an arbitrary EFG to a simple one with isomorphic state space.

The purpose of this note is to provide a characterization of simple edge firing games. The characterization will emerge from a more general result which determines how often a particular vertex can be fired in such a game.

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