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In this paper, we study two kinds of combinatorial objects, generalized integer partitions and tilings of -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 -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.
@article{ITA_2002__36_4_389_0,
author = {Latapy, Matthieu},
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/}
}
TY - JOUR AU - Latapy, Matthieu TI - Integer partitions, tilings of $2D$-gons and lattices JO - RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications PY - 2002 SP - 389 EP - 399 VL - 36 IS - 4 PB - EDP-Sciences UR - http://geodesic.mathdoc.fr/articles/10.1051/ita:2003004/ DO - 10.1051/ita:2003004 LA - en ID - ITA_2002__36_4_389_0 ER -
%0 Journal Article %A Latapy, Matthieu %T Integer partitions, tilings of $2D$-gons and lattices %J RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications %D 2002 %P 389-399 %V 36 %N 4 %I EDP-Sciences %U http://geodesic.mathdoc.fr/articles/10.1051/ita:2003004/ %R 10.1051/ita:2003004 %G en %F ITA_2002__36_4_389_0
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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