Extremal words in morphic subshifts

Luca Q. Zamboni (1, 2) , Rampersad Narad , James Currie , Saari Kalle

1 CTN - Combinatoire, théorie des nombres
2 ICJ - Institut Camille Jordan

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 guarantee 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 a new proof of the form of the lexicographically least word in the shift orbit closure of the Rudin-Shapiro word

Domaines: Combinatoire [math.CO]

Luca Q. Zamboni, Rampersad Narad, James Currie, Saari Kalle. Extremal words in morphic subshifts. Discrete Mathematics, 2014, 322, pp.53-60. ⟨10.1016/j.disc.2014.01.002⟩. ⟨hal-00943571⟩