On growth and fluctuation of k-abelian complexity

Julien Cassaigne (1) , Juhani Karhumaki (2) , Aleksi Saarela (2)

1 I2M - Institut de Mathématiques de Marseille
2 Department of Mathematics and Statistics, University of Turku

An extension of abelian complexity, so called k-abelian complexity, has been considered recently in a number of articles. This paper considers two particular aspects of this extension: First, how much the complexity can increase when moving from a level k to the next one. Second, how much the complexity of a given word can fluctuate. For both questions we give optimal solutions.

Mots clés: AVOIDABILITY; WORDS; SYMBOLIC DYNAMICS; PERIODICITY; EQUIVALENCE

Domaines: Combinatoire [math.CO]

Julien Cassaigne, Juhani Karhumaki, Aleksi Saarela. On growth and fluctuation of k-abelian complexity. European Journal of Combinatorics, 2017, 65, pp.92 - 105. ⟨10.1016/j.ejc.2017.05.006⟩. ⟨hal-01622267⟩