Extremal words in morphic subshifts

نویسندگان

James D. Currie

Narad Rampersad

Kalle Saari

Luca Q. Zamboni

چکیده

Given an infinite word x over an alphabet A, a letter b occurring in x, and a total order σ on A, we call the smallest word with respect to σ starting with b in the shift orbit closure of x an extremal word of x. In this paper we consider the extremal words of morphic words. If x = g(fω(a)) for some morphisms f and g, we give two simple conditions on f and g that guarantees that all extremal words are morphic. This happens, in particular, when x is a primitive morphic or a binary pure morphic word. Our techniques provide characterizations of the extremal words of the Period-doubling word and the Chacon word and give a new proof of the form of the lexicographically least word in the shift orbit closure of the Rudin-Shapiro word. keywords: Lexicographic order, morphic word, primitive morphic word, extremal word, Period-doubling word, Chacon word, Rudin-Shapiro word [email protected] [email protected] [email protected] [email protected]

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