The commutation with ternary sets of words
نویسندگان
چکیده
We prove that for any nonperiodic set of words F ⊆ Σ with at most three elements, the centralizer of F , i.e., the largest set commuting with F , is F ∗. Moreover, any set X commuting with F is of the form X = F I , for some I ⊆ N. A boundary point is thus established, as these results do not hold for all languages with at least four words. This solves a conjecture of Karhumäki and Petre, 2000, and provides positive answers to special cases of some intriguing questions on commutation of languages, raised by Ratoandromanana, 1989 and Conway, 1971.
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