Groups and tilings

AbstractWe 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