Periodicity of one-dimensional tilings
The tiling problem is closely connected with a number of problems of information theory. We show that the Wang-Moore conjecture is valid for the one dimensional case. Namely, any set of templates which permits a tiling of the set ℤ of integers also permits a periodic tiling. We also show that any tiling of ℤ by one template is necessarily periodic. The obtained results are also valid for tiling of the set IR of real numbers.
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