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

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

2001-10-21

arxiv.org/abs/math/0110237v1

Mathematics

Combinatorics

36 pages, 61 figures. To be published in Theoretical Computer Science (special issue on tilings.)

Scientific paper

We first show that the tilings of a general domain form a lattice 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.

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