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arXiv · 1301.4972

Extremal words in morphic subshifts

James D. Currie·Narad Rampersad·Kalle Saari·Luca Q. Zamboni
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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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James D. Currie, Narad Rampersad, Kalle Saari, Luca Q. Zamboni. 2013-01-21. Extremal words in morphic subshifts. https://arxiv.org/abs/1301.4972

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