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Two sided Sand Piles Model and unimodal sequences

Thi Ha Duong Phan — 2008

RAIRO - Theoretical Informatics and Applications

We introduce natural generalizations of two well-known dynamical systems, the Sand Piles Model and the Brylawski's model. We describe their order structure, their reachable configuration's characterization, their fixed points and their maximal and minimal length's chains. Finally, we present an induced model generating the set of unimodal sequences which amongst other corollaries, implies that this set is equipped with a lattice structure.

Signed Chip Firing Games and symmetric Sandpile Models on the cycles

Robert Cori;  Thi Ha Duong Phan;  Thi Thu Huong Tran — 2013

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

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.

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