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Two sided Sand Piles Model and unimodal sequences

Published online by Cambridge University Press:  03 June 2008

Thi Ha Duong Phan*
Affiliation:
LIAFA Université Denis Diderot, Paris 7 - Case 7014-2, Place Jussieu- 75256 Paris Cedex 05-France and Institute of Mathematics, 18 Hoang Quoc Viet, Hanoi, Vietnam; phan@liafa.jussieu.fr phanhaduong@math.ac.vn
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Abstract

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.

Type
Research Article
Copyright
© EDP Sciences, 2008

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