Integer Partitions, Tilings of 2D-gons and Lattices
LIAFA, Université Paris 7, 2 place Jussieu, 75005 Paris, France; email@example.com.
Accepted: December 2002
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.
Mathematics Subject Classification: 05A17 / 11P81 / 05B45 / 06B99 / 06D99 / 68R05 / 52C20 / 52C23 / 52C40
Key words: Integer partitions / tilings of 2D-gons / lattices / Sand Pile Model discrete dynamical models.
© EDP Sciences, 2002