A1 Vertaisarvioitu alkuperäisartikkeli tieteellisessä lehdessä
Abelian periods of factors of Sturmian words
Tekijät: Peltomäki Jarkko
Kustantaja: Academic Press
Julkaisuvuosi: 2020
Journal: Journal of Number Theory
Vuosikerta: 214
Aloitussivu: 251
Lopetussivu: 285
Sivujen määrä: 35
ISSN: 0022-314X
eISSN: 1096-1658
DOI: https://doi.org/10.1016/j.jnt.2020.04.007
Verkko-osoite: https://doi.org/10.1016/j.jnt.2020.04.007
Rinnakkaistallenteen osoite: https://research.utu.fi/converis/portal/detail/Publication/47270763
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.
Ladattava julkaisu This is an electronic reprint of the original article. |