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Substitutions with cofinal fixed points. (English) Zbl 1121.68092

Summary: Let \(\varphi \) be a substitution over a 2-letter alphabet, say \(\{a,b\}\). If \(\varphi (a)\) and \(\varphi (b)\) begin with \(a\) and \(b\) respectively, \(\varphi \) has two fixed points beginning with \(a\) and \(b\) respectively. We characterize substitutions with two cofinal fixed points (i.e., which differ only by prefixes). The proof is a combinatorial one, based on the study of repetitions of words in the fixed points.

MSC:

68R15 Combinatorics on words
11B85 Automata sequences
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References:

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