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.
- Publication:
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arXiv Mathematics e-prints
- Pub Date:
- October 1998
- DOI:
- 10.48550/arXiv.math/9810024
- arXiv:
- arXiv:math/9810024
- Bibcode:
- 1998math.....10024C
- Keywords:
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- Mathematics - Combinatorics