A1 Refereed original research article in a scientific journal

Abelian periods of factors of Sturmian words




AuthorsPeltomäki Jarkko

PublisherAcademic Press

Publication year2020

JournalJournal of Number Theory

Volume214

First page 251

Last page285

Number of pages35

ISSN0022-314X

eISSN1096-1658

DOIhttps://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 addresshttps://research.utu.fi/converis/portal/detail/Publication/47270763(external)


Abstract

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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Last updated on 2024-26-11 at 22:12