Signed Chip Firing Games and symmetric Sandpile Models on the cycles∗
1 Labri, University Bordeaux
2 Institute of Mathematics, 18 Hoang Quoc Viet, Cau Giay district, Hanoi, Vietnam.
Accepted: 7 August 2012
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.
Mathematics Subject Classification: 05C57 / 91A43 / 68R15 / 68Rxx
Key words: Sandpile Model / Chip Firing Game / circular distribution / Symmetric Sandpile Model / Signed Chip Firing Game / lattice structure
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