Abstract:
We use this technique to construct an example of an infinite finitely related nilsemigroup, which gives an answer to the question of L.N.Shvernik. In this construction each paths on a tiling becomes an element of a semigroup, and the structure of the tiling corresponds to the algebraic relations in this semigroup. A tiling should respect only a finite number of local constraints, which correspond to a finite number of relators in the semigroup. This construction is connected with the Goodman-Strauss theorem on aperiodic hierarchical tilings.
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