A one-dimensional tiling is a bi-infinite string on a finite alphabet, and its tiling semigroup is an inverse semigroup whose elements are marked finite substrings of the tiling. We characterize the structure of these semigroups in the periodic case, in which the tiling is obtained by repetition of a fixed primitive word.
- inverse semigroups
Dombi, E., & Gilbert, N. D. (2009). The tiling semigroups of one-dimensional periodic tilings. Journal of the Australian Mathematical Society, 87(2), 153-160. https://doi.org/10.1017/S144678870800075X