Combinatorical and Algebraic Structures Seminar

Session details

Date: 13.11.2018
Speaker: Élise Vandomme, FJFI, České vysoké učení technické v Praze
Title: New notions of recurrence in a multidimensional setting
Abstract: In one dimension, an infinite word is said to be recurrent if every prefix occurs at least twice. A straightforward extension of this definition in higher dimensions turns out to be rather unsatisfying. In this talk, we present several notions of recurrence in the multidimensional case. In particular, we are interested in words having the property to be strongly uniformly recurrent: for each direction $\mathbf{q}$, every prefix occurs in that direction (i.e. in positions $i\mathbf{q}$) with bounded gaps. We will provide several constructions of such words and focus on the strongly uniform recurrence in the case of square morphisms.

Return to index.