A note on abelian returns in rotation words

[en] Pursuing the study started by Rigo, Salimov and Vandomme, we use elementary number-theoretic techniques to characterize rotation words having a finite set of abelian returns to all prefixes. We also make the connection between the three gap theorem and the number of semi-abelian returns for Sturmian words, simplifying some arguments developed by Puzynina and Zamboni.

Disciplines :

Mathematics

Author, co-author :

Rampersad, Narad

Rigo, Michel ; Université de Liège - ULiège > Département de mathématique > Mathématiques discrètes

Salimov, Pavel ; Université de Liège - ULiège > Département de mathématique > Mathématiques discrètes

Language :

English

Title :

A note on abelian returns in rotation words

Publication date :

2014

Journal title :

Theoretical Computer Science

ISSN :

0304-3975

Publisher :

Elsevier Science, Amsterdam, Netherlands

Volume :

528

Pages :

101-107

Peer reviewed :

Peer Reviewed verified by ORBi

Available on ORBi :

since 03 December 2012

Statistics

Number of views

261 (21 by ULiège)

Number of downloads

241 (9 by ULiège)

More statistics

Scopus citations^®

Scopus citations^®
without self-citations

OpenCitations

OpenAlex citations

publications

supporting

mentioning

contrasting

Smart Citations

Citing PublicationsSupportingMentioningContrasting

View Citations

See how this article has been cited at scite.ai

scite shows how a scientific paper has been cited by providing the context of the citation, a classification describing whether it supports, mentions, or contrasts the cited claim, and a label indicating in which section the citation was made.

Bibliography

B. Adamczewski Codages de rotations et phénomènes d'autosimilarité J. Théor. Nombres Bordeaux 14 2002 351 386
B. Adamczewski Balances for fixed points of primitive substitutions Theoret. Comput. Sci. 307 2003 47 75
P. Alessandri, and V. Berthé Three distance theorems and combinatorics on words Enseign. Math. (2) 44 1998 103 132
M. Bucci, A. De Luca, and L.Q. Zamboni Reversible Christoffel factorizations Theoret. Comput. Sci. 495 2013 17 24
G. Didier Combinatoire des codages de rotations Acta Arith. 85 1998 157 177
H. Kesten On a conjecture of Erdos and Szüsz related to uniform distribution mod 1 Acta Arith. 12 1966/1967 193 212
M. Lothaire Algebraic Combinatorics on Words Encyclopedia Math. Appl. vol. 90 2002 Cambridge University Press
S. Puzynina, and L.Q. Zamboni Abelian returns in Sturmian words J. Combin. Theory Ser. A 120 2013 390 408
G. Richomme, K. Saari, and L.Q. Zamboni Abelian complexity in minimal subshifts J. Lond. Math. Soc. 83 2010 79 95
M. Rigo, P. Salimov, and E. Vandomme Some properties of abelian return words J. Integer Seq. 16 2013 13.2.5

Similar publications

Sorry the service is unavailable at the moment. Please try again later.