English

The Symbolic Dynamics of Tiling the Integers

Combinatorics 2007-05-23 v1

Abstract

A finite collection PP of finite sets tiles the integers iff the integers can be expressed as a disjoint union of translates of members of PP. We associate with such a tiling a doubly infinite sequence with entries from PP. 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}
}