Abelian periods of factors of Sturmian words
Peltomäki Jarkko
Abelian periods of factors of Sturmian words
Peltomäki Jarkko
Academic Press
Julkaisun pysyvä osoite on:
https://urn.fi/URN:NBN:fi-fe2021042822052
https://urn.fi/URN:NBN:fi-fe2021042822052
Tiivistelmä
We study the abelian period sets of Sturmian words, which are codings of irrational rotations on a one-dimensional torus. The main result states that the minimum abelian period of a factor of a Sturmian word of angle α with continued fraction expansion [0; a1, a2, ...] is either tqk with 1 ≤ t ≤ ak+1 (a multiple of a denominator qk of a convergent of α) or qk,l (a denominator qk,l of a semiconvergent of α). This result generalizes a result of Fici et al. stating that the abelian period set of the Fibonacci word is the set of Fibonacci numbers. A characterization of the Fibonacci word in terms of its abelian period set is obtained as a corollary.
Kokoelmat
- Rinnakkaistallenteet [19207]