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Integer Partitions, Tilings of 2D-gons and Lattices

Published online by Cambridge University Press:  15 February 2003

Matthieu Latapy*
Affiliation:
LIAFA, Université Paris 7, 2 place Jussieu, 75005 Paris, France; latapy@liafa.jussieu.fr.
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Abstract

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.

Type
Research Article
Copyright
© EDP Sciences, 2002

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