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Coincidence for substitutions of Pisot type. (English) Zbl 1028.37008
A substitution $$\sigma$$ on a finite alphabet satisfies the strong coincidence condition if for every letters $$i$$ and $$j$$ of the alphabet, there exist integers $$n, k$$ such that $$\sigma^n(i)$$ and $$\sigma^n(k)$$ have the same $$k$$th letter, and their prefixes of length $$k-1$$ contain the same number of occurrence of each letter. In the case in which the dominant eigenvalue of the transition matrix of the substitution is a Pisot number, the authors prove that all substitutions on two letters satisfy the strong coincidence condition, and obtain a partial result for substitutions on more than two letters.

MSC:
 37B10 Symbolic dynamics
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