Article (Scientific journals)
On non-repetitive complexity of Arnoux–Rauzy words
Medková, K.; Pelantová, E.; Vandomme, Elise
2020In Discrete Applied Mathematics, 285, p. 423-433
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Keywords :
Arnoux–Rauzy word; Directive sequence; Factor complexity; Non-repetitivity; Combinatorial mathematics; Infinite word; Return words; Mathematical techniques
Abstract :
[en] The non-repetitive complexity nrCu and the initial non-repetitive complexity inrCu are functions which reflect the structure of the infinite word u with respect to the repetitions of factors of a given length. We determine nrCu for the Arnoux–Rauzy words and inrCu for the standard Arnoux–Rauzy words. Our main tools are the S-adic representation of Arnoux–Rauzy words and a description of return words to their factors. The formulas we obtain are then used to evaluate nrCu and inrCu for the d-bonacci word. © 2020 Elsevier B.V.
Disciplines :
Mathematics
Author, co-author :
Medková, K.;  Department of Mathematics, FNSPE, Czech Technical University in Prague, Trojanova 13, Praha 2, 120 00, Czech Republic
Pelantová, E.;  Department of Mathematics, FNSPE, Czech Technical University in Prague, Trojanova 13, Praha 2, 120 00, Czech Republic
Vandomme, Elise ;  Université de Liège - ULiège
Language :
English
Title :
On non-repetitive complexity of Arnoux–Rauzy words
Publication date :
2020
Journal title :
Discrete Applied Mathematics
ISSN :
0166-218X
eISSN :
1872-6771
Publisher :
Elsevier, Amsterdam, Netherlands
Volume :
285
Pages :
423-433
Peer reviewed :
Peer Reviewed verified by ORBi
Available on ORBi :
since 27 August 2021

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