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Two sided Sand Piles Model and unimodal sequences
Thi Ha Duong Phan
Journal:

RAIRO - Theoretical Informatics and Applications / Volume 42 / Issue 3 / July 2008

Published online by Cambridge University Press:

03 June 2008, pp. 631-646

Print publication:

July 2008
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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.