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.


37B10 Symbolic dynamics
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