Integer Partitions, Tilings of 2D-gons and Lattices
Published online by Cambridge University Press: 15 February 2003
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.
- Research Article
- RAIRO - Theoretical Informatics and Applications , Volume 36 , Issue 4 , October 2002 , pp. 389 - 399
- © EDP Sciences, 2002