Avoidability of long $k$-abelian repetitions - LIRMM - Laboratoire d’Informatique, de Robotique et de Microélectronique de Montpellier
Journal Articles Mathematics of Computation Year : 2016

Avoidability of long $k$-abelian repetitions

Abstract

We study the avoidability of long $k$-abelian-squares and $k$-abelian-cubes on binary and ternary alphabets. For $k$= 1, these are Mäkelä’s questions. We show that one cannot avoid abelian-cubes of abelian period at least $2$ in infinite binary words, and therefore answering negatively one question from Mäkelä. Then we show that one can avoid $3$-abelian-squares of period at least $3$ in infinite binary words and $2$-abelian-squares of period at least $2$ in infinite ternary words. Finally, we study the minimum number of distinct $k$-abelian-squares that must appear in an infinite binary word.
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lirmm-04659496 , version 1 (24-07-2024)

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Michaël Rao, Matthieu Rosenfeld. Avoidability of long $k$-abelian repetitions. Mathematics of Computation, 2016, 85 (302), pp.3051-3060. ⟨10.1090/mcom/3085⟩. ⟨lirmm-04659496⟩
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