The Symbolic Dynamics of Tiling the Integers
Combinatorics
2007-05-23 v1
Abstract
A finite collection of finite sets tiles the integers iff the integers can be expressed as a disjoint union of translates of members of . We associate with such a tiling a doubly infinite sequence with entries from . 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.
Keywords
Cite
@article{arxiv.math/9810024,
title = {The Symbolic Dynamics of Tiling the Integers},
author = {Ethan M. Coven and William Geller and Sylvia Silberger and William P. Thurston},
journal= {arXiv preprint arXiv:math/9810024},
year = {2007}
}