A1 Refereed original research article in a scientific journal
Abelian periods of factors of Sturmian words
Authors: Peltomäki Jarkko
Publisher: Academic Press
Publication year: 2020
Journal: Journal of Number Theory
Volume: 214
First page : 251
Last page: 285
Number of pages: 35
ISSN: 0022-314X
eISSN: 1096-1658
DOI: https://doi.org/10.1016/j.jnt.2020.04.007(external)
Web address : https://doi.org/10.1016/j.jnt.2020.04.007(external)
Self-archived copy’s web address: https://research.utu.fi/converis/portal/detail/Publication/47270763(external)
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.
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