RAIRO - Theoretical Informatics and Applications

Research Article

Integer Partitions, Tilings of 2D-gons and Lattices

Matthieu Latapy

LIAFA, Université Paris 7, 2 place Jussieu, 75005 Paris, France; latapy@liafa.jussieu.fr.

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.

(Received July 2002)

(Accepted December 2002)

(Online publication February 15 2003)

Key Words:

  • Integer partitions;
  • tilings of 2D-gons;
  • lattices;
  • Sand Pile Model discrete dynamical models.

Mathematics Subject Classification:

  • 05A17;
  • 11P81;
  • 05B45;
  • 06B99;
  • 06D99;
  • 68R05;
  • 52C20;
  • 52C23;
  • 52C40
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