Extremal words in morphic subshifts
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.
Cite
@article{arxiv.1301.4972,
title = {Extremal words in morphic subshifts},
author = {James D. Currie and Narad Rampersad and Kalle Saari and Luca Q. Zamboni},
journal= {arXiv preprint arXiv:1301.4972},
year = {2013}
}
Comments
Replaces a previous version entitled "Extremal words in the shift orbit closure of a morphic sequence" with an added result on primitive morphic sequences. Submitted