Standard

On the rigidity of Arnoux-Rauzy words. / Berthe, Valerie; Пузынина, Светлана Александровна.

In: Advances in Applied Mathematics, Vol. 170, 102932, 12.2025.

Research output: Contribution to journal › Article › peer-review

Harvard

Berthe, V & Пузынина, СА 2025, 'On the rigidity of Arnoux-Rauzy words', Advances in Applied Mathematics, vol. 170, 102932. https://doi.org/10.1016/j.aam.2025.102932

APA

Berthe, V., & Пузынина, С. А. (2025). On the rigidity of Arnoux-Rauzy words. Advances in Applied Mathematics, 170, [102932]. https://doi.org/10.1016/j.aam.2025.102932

Vancouver

Berthe V, Пузынина СА. On the rigidity of Arnoux-Rauzy words. Advances in Applied Mathematics. 2025 Dec;170. 102932. https://doi.org/10.1016/j.aam.2025.102932

Author

Berthe, Valerie ; Пузынина, Светлана Александровна. / On the rigidity of Arnoux-Rauzy words. In: Advances in Applied Mathematics. 2025 ; Vol. 170.

BibTeX

@article{10014470b75b4070b2b1d5eda4188374,
title = "On the rigidity of Arnoux-Rauzy words",
abstract = "An infinite word generated by a substitution is rigid if all the substitutions which fix this word are powers of the same substitution. Sturmian words as well as characteristic Arnoux-Rauzy words that are generated by iterating a substitution are known to be rigid. In the present paper, we prove that all Arnoux-Rauzy words generated by iterating a substitution are rigid. The proof relies on two main ingredients: first, the fact that the primitive substitutions that fix an Arnoux-Rauzy word share a common power, and secondly, the notion of normal form of an episturmian substitution (i.e., a substitution that fixes an Arnoux-Rauzy word). The main difficulty is then of a combinatorial nature and relies on the normalization process when taking powers of episturmian substitutions: the normal form of a square is not necessarily equal to the square of the normal forms.",
keywords = "Arnoux-Rauzy words, Episturmian words, Rigidity, Substitutions",
author = "Valerie Berthe and Пузынина, {Светлана Александровна}",
year = "2025",
month = dec,
doi = "10.1016/j.aam.2025.102932",
language = "English",
volume = "170",
journal = "Advances in Applied Mathematics",
issn = "0196-8858",
publisher = "Elsevier",

}

RIS

TY - JOUR

T1 - On the rigidity of Arnoux-Rauzy words

AU - Berthe, Valerie

AU - Пузынина, Светлана Александровна

PY - 2025/12

Y1 - 2025/12

N2 - An infinite word generated by a substitution is rigid if all the substitutions which fix this word are powers of the same substitution. Sturmian words as well as characteristic Arnoux-Rauzy words that are generated by iterating a substitution are known to be rigid. In the present paper, we prove that all Arnoux-Rauzy words generated by iterating a substitution are rigid. The proof relies on two main ingredients: first, the fact that the primitive substitutions that fix an Arnoux-Rauzy word share a common power, and secondly, the notion of normal form of an episturmian substitution (i.e., a substitution that fixes an Arnoux-Rauzy word). The main difficulty is then of a combinatorial nature and relies on the normalization process when taking powers of episturmian substitutions: the normal form of a square is not necessarily equal to the square of the normal forms.

AB - An infinite word generated by a substitution is rigid if all the substitutions which fix this word are powers of the same substitution. Sturmian words as well as characteristic Arnoux-Rauzy words that are generated by iterating a substitution are known to be rigid. In the present paper, we prove that all Arnoux-Rauzy words generated by iterating a substitution are rigid. The proof relies on two main ingredients: first, the fact that the primitive substitutions that fix an Arnoux-Rauzy word share a common power, and secondly, the notion of normal form of an episturmian substitution (i.e., a substitution that fixes an Arnoux-Rauzy word). The main difficulty is then of a combinatorial nature and relies on the normalization process when taking powers of episturmian substitutions: the normal form of a square is not necessarily equal to the square of the normal forms.

KW - Arnoux-Rauzy words

KW - Episturmian words

KW - Rigidity

KW - Substitutions

UR - https://www.mendeley.com/catalogue/f0cd5d25-b446-3a0d-8b70-781db6a2bd82/

U2 - 10.1016/j.aam.2025.102932

DO - 10.1016/j.aam.2025.102932

M3 - Article

VL - 170

JO - Advances in Applied Mathematics

JF - Advances in Applied Mathematics

SN - 0196-8858

M1 - 102932

ER -

ID: 141444648