The Commutation With Codes and Ternary Sets of Words (2002)
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BibTeX
@MISC{Karhumäki02thecommutation,
author = {Juhani Karhumäki and Michel Latteux and Ion Petre and Michel Latteux},
title = {The Commutation With Codes and Ternary Sets of Words},
year = {2002}
}
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Abstract
We prove several results on the commutation of languages. First, we prove that the largest set commuting with a given code X , i.e., its centralizer C(X), is always (X) , where (X) is the primitive root of X . Using this result, we characterize the commutation with codes similarly as for words, polynomials, and formal power series: a language commutes with X if and only if it is a union of powers of (X). This solves a conjecture of Ratoandromanana, 1989, and also gives an armative answer to a special case of an intriguing problem raised by Conway in 1971. Second, we prove that for any nonperiodic ternary set of words F , and moreover, a language commutes with F if and only if it is a union of powers of F , results previously known only for ternary codes. A boundary point is thus established, as these results do not hold for languages with at least four words.
