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Extremal words in morphic subshifts

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Author

Zamboni, Luca Q.
Saari, Kalle
Rampersad, Narad
Currie, James D.

Uri

http://hdl.handle.net/10680/1763

Date

2014-01-22

Doi

10.1016/j.disc.2014.01.002

Citation

Discrete Math. 322 (2014) 53-60

Abstract

Given an infinite word x over an alphabet A, a letter b occurring in x, and a total order \sigma on A, we call the smallest word with respect to \sigma 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(f^\omega(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.

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