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Integer Partitions, Tilings of 2D-gons and Lattices

Published online by Cambridge University Press:  15 February 2003

Matthieu Latapy*
LIAFA, Université Paris 7, 2 place Jussieu, 75005 Paris, France;
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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.

Research Article
© EDP Sciences, 2002

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