Binomial Complexities and Parikh-Collinear Morphisms

[en] Two words are k-binomially equivalent, if each word of length at most k occurs as a subword, or scattered factor, the same number of times in both words. The k-binomial complexity of an infinite word maps the natural n to the number of k-binomial equivalence classes represented by its factors of length n. Inspired by questions raised by Lejeune, we study the relationships between the k and (k+1)-binomial complexities; as well as the link with the usual factor complexity. We show that pure morphic words obtained by iterating a Parikh-collinear morphism, i.e. a morphism mapping all words to words with bounded abelian complexity, have bounded k-binomial complexity. In particular, we study the properties of the image of a Sturmian word by an iterate of the Thue-Morse morphism.

Disciplines :

Mathematics

Author, co-author :

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

Stipulanti, Manon ; Université de Liège - ULiège > Département de mathématique > Mathématiques discrètes

Whiteland, Markus ; Université de Liège - ULiège > Département de mathématique > Mathématiques discrètes

Language :

English

Title :

Binomial Complexities and Parikh-Collinear Morphisms

Publication date :

2022

Event name :

Developments in Language Theory

Event date :

du 9 mai 2022 au 13 mai 2022

Audience :

International

Journal title :

Lecture Notes in Computer Science

ISSN :

0302-9743

eISSN :

1611-3349

Publisher :

Springer, Heidelberg, Germany

Volume :

13257

Pages :

251-262

Peer reviewed :

Peer reviewed

Funders :

F.R.S.-FNRS - Fonds de la Recherche Scientifique

Available on ORBi :

since 13 January 2022

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Bibliography

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