Abstract
A finite collectionP of finite sets tiles the integers iff the integers can be expressed as a disjoint union of translates of members ofP. We associate with such a tiling a doubly infinite sequence with entries fromP. 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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Some of this work was done at the Mathematical Sciences Research Institute (MSRI), where research is supported in part by NSF grant DMS-9701755. The first two authors thank K. Schmidt for useful conversations and ideas.
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Coven, E.M., Geller, W., Silberger, S. et al. The symbolic dynamics of tiling the integers. Isr. J. Math. 130, 21–27 (2002). https://doi.org/10.1007/BF02764069
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DOI: https://doi.org/10.1007/BF02764069