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Integer Partitions, Tilings of 2D-gons and Lattices

Published online by Cambridge University Press:  15 February 2003

Matthieu Latapy
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.

Keywords

Integer partitionstilings of 2D-gonslatticesSand Pile Model discrete dynamical models.
Type
Research Article
Information
RAIRO - Theoretical Informatics and Applications , Volume 36 , Issue 4 , October 2002 , pp. 389 - 399
Copyright
© EDP Sciences, 2002

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