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Abelian periods of factors of Sturmian words




TekijätPeltomäki Jarkko

KustantajaAcademic Press

Julkaisuvuosi2020

JournalJournal of Number Theory

Vuosikerta214

Aloitussivu251

Lopetussivu285

Sivujen määrä35

ISSN0022-314X

eISSN1096-1658

DOIhttps://doi.org/10.1016/j.jnt.2020.04.007

Verkko-osoitehttps://doi.org/10.1016/j.jnt.2020.04.007

Rinnakkaistallenteen osoitehttps://research.utu.fi/converis/portal/detail/Publication/47270763


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.


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