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tilings of 2d-gons

RAIRO - Theoretical Informatics and Applications (1)

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Integer Partitions, Tilings of 2D-gons and Lattices
Matthieu Latapy
Journal:

RAIRO - Theoretical Informatics and Applications / Volume 36 / Issue 4 / October 2002

Published online by Cambridge University Press:

15 February 2003, pp. 389-399

Print publication:

October 2002
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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.