A presentation for one-dimensional tiling semigroups

Tiling semigroups were first considered by J. Kellendonk and M. Lawson following the work of Kellendonk regarding the modelling of solids using gap labelling. In this talk, we will give a presentation for the inverse semigroup associated with a factorial language, which is a generalization of the tiling semigroup of a one-dimensional tiling, and discuss some conditions on the tiling in order for the presentation to be finite. This is a joint work with D. B. McAlister.