Abelian periods of factors of Sturmian words
| Autor: | Jarkko Peltomäki |
|---|---|
| Rok vydání: | 2020 |
| Předmět: |
FOS: Computer and information sciences
Algebra and Number Theory Fibonacci number Mathematics - Number Theory Formal Languages and Automata Theory (cs.FL) 68R15 11A55 010102 general mathematics Sturmian word Computer Science - Formal Languages and Automata Theory Torus 010103 numerical & computational mathematics Characterization (mathematics) 01 natural sciences Combinatorics Irrational number FOS: Mathematics Number Theory (math.NT) 0101 mathematics Abelian group Continued fraction Fibonacci word Computer Science::Formal Languages and Automata Theory Mathematics |
| Zdroj: | Journal of Number Theory. 214:251-285 |
| ISSN: | 0022-314X |
| Popis: | 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 $\alpha$ with continued fraction expansion $[0; a_1, a_2, \ldots]$ is either $tq_k$ with $1 \leq t \leq a_{k+1}$ (a multiple of a denominator $q_k$ of a convergent of $\alpha$) or $q_{k,\ell}$ (a denominator $q_{k,\ell}$ of a semiconvergent of $\alpha$). 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. Comment: 27 pages, 3 figures |
| Databáze: | OpenAIRE |
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