An algorithm to generate exactly once every tiling with lozenges of a domain
Abstract
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.
- Publication:
-
arXiv Mathematics e-prints
- Pub Date:
- October 2001
- DOI:
- 10.48550/arXiv.math/0110237
- arXiv:
- arXiv:math/0110237
- Bibcode:
- 2001math.....10237D
- Keywords:
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- Mathematics - Combinatorics;
- 05A15
- E-Print:
- 36 pages, 61 figures. To be published in Theoretical Computer Science (special issue on tilings.)