On abelian saturated infinite words
Aleksi Saarela; Juhani Karhumäki; Sergey Avgustinovich; Julien Cassaigne; Svetlana Puzynina
On abelian saturated infinite words
Aleksi Saarela
Juhani Karhumäki
Sergey Avgustinovich
Julien Cassaigne
Svetlana Puzynina
Elsevier
Julkaisun pysyvä osoite on:
https://urn.fi/URN:NBN:fi-fe2021042719300
https://urn.fi/URN:NBN:fi-fe2021042719300
Tiivistelmä
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 n2-saturated, but, for any ε>0, they can be abelian n2−ε-saturated. There is also a sequence of finite words (wn), with |wn|=n, such that each wn contains at least Cn2 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.
Kokoelmat
- Rinnakkaistallenteet [19207]