The symbolic dynamics of tiling the integers

Abstract

A finite collection P of finite sets tiles the integers iff the integers can be expressed as a disjoint union of translates of members of P. We associate with such a tiling a doubly infinite sequence with entries from P. The set of all such sequences is a sofic system, called a tiling system. We show that, up to powers of the shift, every shift of finite type can be realized as a tiling system.

Homéomorphismes et nombre d'intersection

“…We mention another paper on tilings (although this word is used in a slightly different meaning), namely, the paper [62], by Coven, Geller, Silberger and Thurston, concerned with the symbolic dynamics of tiling the integers. Here, a finite collection of finite sets of integers is said to "tile the integers" if the set of all integers can be written as a disjoint union of translates of elements of this finite set.…”