In this article, we investigate some further properties of one-dimensional tiling semigroups as a particular case of the inverse semigroup associated with a factorial language. Namely, a presentation for the semigroup and its description as a P∗-semigroup are obtained. Since both constructions rely on the language, these properties highlight the deep connection between the semigroup and the language associated with a one-dimensional tiling semigroup.

CEMAT - Center for Computational and Stochastic Mathematics