Geodesic
Integer partitions, tilings of 2D-gons and lattices
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 36 (2002) no. 4, pp. 389-399

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In this paper, we study two kinds of combinatorial objects, generalized integer partitions and tilings of 2D-gons (hexagons, octagons, decagons, etc.). We show that the sets of partitions, ordered with a simple dynamics, have the distributive lattice structure. Likewise, we show that the set of tilings of a 2D-gon is the disjoint union of distributive lattices which we describe. We also discuss the special case of linear integer partitions, for which other dynamical models exist.

DOI : 10.1051/ita:2003004
Classification : 05A17, 11P81, 05B45, 06B99, 06D99, 68R05, 52C20, 52C23, 52C40
Keywords: integer partitions, tilings of $2D$-gons, lattices, sand pile model, discrete dynamical models 
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     title = {Integer partitions, tilings of $2D$-gons and lattices},
     journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications},
     pages = {389--399},
     publisher = {EDP-Sciences},
     volume = {36},
     number = {4},
     year = {2002},
     doi = {10.1051/ita:2003004},
     mrnumber = {1965424},
     zbl = {1028.05010},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/ita:2003004/}
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Latapy, Matthieu. Integer partitions, tilings of $2D$-gons and lattices. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 36 (2002) no. 4, pp. 389-399. doi: 10.1051/ita:2003004

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