The Symbolic Dynamics of Tiling the Integers

Details The Symbolic Dynamics of Tiling the Integers The Symbolic Dynamics of Tiling the Integers

1998-10-05

arxiv.org/abs/math/9810024v1

Mathematics

Combinatorics

Scientific paper

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.

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