On abelian saturated infinite words
Résumé
Let f : Z + → R be an increasing function. We say that an infinite word w is abelian f (n)-saturated if each factor of length n contains Θ(f (n)) abelian nonequivalent factors. We show that binary infinite words cannot be abelian n 2saturated, but, for any ε > 0, they can be abelian n 2−ε-saturated. There is also a sequence of finite words (w n), with |w n | = n, such that each w n contains at least Cn 2 abelian nonequivalent factors for some constant C > 0. We also consider saturated words and their connection to palindromic richness in the case of equality and k-abelian equivalence.
Domaines
Mathématique discrète [cs.DM]
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