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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
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.

Keywords

Discrete dynamical systemSand Piles Modelpartitionunimodal sequenceorderlatticedominance orderingfixed point.
Type
Research Article
Information
RAIRO - Theoretical Informatics and Applications , Volume 42 , Issue 3: JM'06 , July 2008 , pp. 631 - 646
Copyright
© EDP Sciences, 2008

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