An algorithm to generate exactly once every tiling with lozenges of a domain

Authors:
Sébastien Desreux
Affiliations:
LIAFA, Université Paris 7, case 7014, 2 place Jussieu, 75 251 Paris Cedex 05, France
Venue:
Theoretical Computer Science - Special issue: Tilings of the plane
Year:
2003

Citing 7
Cited 2

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Abstract

We first show that the tilings of a domain D form a lattice (using the same kind of arguments as in (Research Report No. 1999-25)) which we then undertake to decompose and generate without any redundance. To this end, we study extensively the relatively simple case of hexagons and their deformations. We show that general domains can be broken up into hexagon-like parts. Finally we give an algorithm to generate exactly once every element in the lattice of the tilings of a general domain D.