Document RAIRO-Theor. Inf. Appl. 42, 631-646 (2008)
DOI: 10.1051/ita:2008019
Two sided Sand Piles Model and unimodal sequences
Thi Ha Duong PHANLIAFA 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
Published online: 3 June 2008
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.
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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