Groups and tilings

Authors:
Danièle Beauquier;Jean-Claude Fournier
Affiliations:
Univ. Paris-12, Creteil, France;Univ. Paris-12, Créteil, France
Venue:
Theoretical Computer Science
Year:
2002

Citing 5
Cited 0

Tilings and patterns

Tilings and patterns
Tiling with Polyominoes and Combinatorial Group Theory

Journal of Combinatorial Theory Series A
Conway's tiling groups

American Mathematical Monthly
Tiling the plane with one tile

SCG '90 Proceedings of the sixth annual symposium on Computational geometry
Tiling with dominoes pictures of plane figures without holes: graphic basis of the Thurston algorithm, parallelization, uniqueness and decomposition

Theoretical Computer Science - Special issue: selected papers from “GASCOM '94” and the “Polyominoes and Tilings” workshops

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Abstract

We prove that the word problem for the group of dominoes is equivalent to the existence of a directed tiling for the corresponding closed curve in the plane, which, in turn is equivalent to the fact that the curve is "balanced". This last property beeing decidable, the word problem is also decidable. Moreover we prove that this result is transposable in any other regular grid (hexagonal or triangular) and we partially extend it to "exact" tiles.