Two sided Sand Piles Model and unimodal sequences
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; email@example.com firstname.lastname@example.org
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.
Mathematics Subject Classification: 68R05 / 05A17
Key words: Discrete dynamical system / Sand Piles Model / partition / unimodal sequence / order / lattice / dominance ordering / fixed point.
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