LIAFA, Université Paris 7, 2 place Jussieu, 75005 Paris, France; email@example.com.
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)
Mathematics Subject Classification: