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Integer Partitions, Tilingsof 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 combinatorialobjects, 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-gonis the disjoint union of distributivelattices which we describe.We also discuss the special case of linear integerpartitions, for which other dynamical models exist.

Keywords

Integer partitionstilings of 2D-gonslatticesSand Pile Modeldiscretedynamical models.

Information

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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