A4 Vertaisarvioitu artikkeli konferenssijulkaisussa
Every nonnegative real number is an abelian critical exponent
Tekijät: Peltomäki Jarkko, Whiteland Markus A.
Toimittaja: Mercaş Robert, Reidenbach Daniel
Konferenssin vakiintunut nimi: International Conference on Combinatorics on Words
Julkaisuvuosi: 2019
Journal: Lecture Notes in Computer Science
Kokoomateoksen nimi: Combinatorics on Words: 12th International Conference, WORDS 2019, Loughborough, UK, September 9–13, 2019, Proceedings
Sarjan nimi: Lecture Notes in Computer Science
Vuosikerta: 11682
Aloitussivu: 275
Lopetussivu: 285
ISBN: 978-3-030-28795-5
eISBN: 978-3-030-28796-2
DOI: https://doi.org/10.1007/978-3-030-28796-2_22
Rinnakkaistallenteen osoite: https://research.utu.fi/converis/portal/detail/Publication/41978810
The abelian critical exponent of an infinite word $w$ is defined as the maximum ratio between the exponent and the period of an abelian power occurring in $w$. It was shown by Fici et al. that the set of finite abelian critical exponents of Sturmian words coincides with the Lagrange spectrum. This spectrum contains every large enough positive real number. We construct words whose abelian critical exponents fill the remaining gaps, that is, we prove that for each nonnegative real number $\theta$ there exists an infinite word having abelian critical exponent $\theta$. We also extend this result to the $k$-abelian setting.
Ladattava julkaisu This is an electronic reprint of the original article. |  |
