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Signed Chip Firing Games and symmetric Sandpile Models on the cycles∗

Published online by Cambridge University Press:  31 October 2012

Robert Cori ,
Thi Ha Duong Phan  and
Thi Thu Huong Tran
Robert Cori
Affiliation:
Labri, University Bordeaux 1, 33405 Talence Cedex, France.. robert.cori@labri.fr
Thi Ha Duong Phan
Affiliation:
Institute of Mathematics, 18 Hoang Quoc Viet, Cau Giay district, Hanoi, Vietnam. ; phanhaduong@math.ac.vn; ttthuong@math.ac.vn
Thi Thu Huong Tran
Affiliation:
Institute of Mathematics, 18 Hoang Quoc Viet, Cau Giay district, Hanoi, Vietnam. ; phanhaduong@math.ac.vn; ttthuong@math.ac.vn
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Abstract

We investigate the Sandpile Model and Chip Firing Game and an extension of these models on cycle graphs. The extended model consists of allowing a negative number of chips at each vertex. We give the characterization of reachable configurations and of fixed points of each model. At the end, we give explicit formula for the number of their fixed points.

Keywords

Sandpile ModelChip Firing Gamecircular distributionSymmetric Sandpile ModelSigned Chip Firing Gamelattice structure
Type
Research Article
Information
RAIRO - Theoretical Informatics and Applications , Volume 47 , Issue 2 , April 2013 , pp. 133 - 146
Copyright
© EDP Sciences 2012

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