Two sided sand piles model and unimodal sequences
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 42 (2008) no. 3, pp. 631-646.

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.

DOI : https://doi.org/10.1051/ita:2008019
Classification : 68R05,  05A17
Mots clés : discrete dynamical system, sand piles model, partition, unimodal sequence, order, lattice, dominance ordering, fixed point
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     author = {Thi Ha Duong Phan},
     title = {Two sided sand piles model and unimodal sequences},
     journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications},
     pages = {631--646},
     publisher = {EDP-Sciences},
     volume = {42},
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     year = {2008},
     doi = {10.1051/ita:2008019},
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     language = {en},
     url = {http://www.numdam.org/articles/10.1051/ita:2008019/}
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Thi Ha Duong Phan. Two sided sand piles model and unimodal sequences. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 42 (2008) no. 3, pp. 631-646. doi : 10.1051/ita:2008019. http://www.numdam.org/articles/10.1051/ita:2008019/

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