Automaticity and Parikh-collinear Morphisms

Rigo, Michel; Stipulanti, Manon; Whiteland, Markus

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Automaticity and Parikh-collinear Morphisms

Rigo, Michel; Stipulanti, Manon; Whiteland, Markus

2023 • In Robert Merças; Anna E. Frid (Eds.) Words 2023

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Keywords :

combinatorics on words; Automatic sequences; Morphic words; Abelian complexity; Automated theorem proving; Walnut

Abstract :

[en] Parikh-collinear morphisms have recently received a lot of attention. They are defined by the property that the Parikh vectors of the images of letters are collinear. We first show that any fixed point of such a morphism is automatic. Consequently, we get under some mild technical assumption that the abelian complexity of a binary fixed point of a Parikh-collinear morphism is also automatic, and we discuss a generalization to arbitrary alphabets. Then, we consider the abelian complexity function of the fixed point of the Parikh-collinear morphism $0\mapsto 010011$, $1\mapsto 1001$. This $5$-automatic sequence is shown to be aperiodic, answering a question of Salo and Sportiello.

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 > Mathematics

Language :

English

Title :

Automaticity and Parikh-collinear Morphisms

Publication date :

2023

Event name :

Words 2023 14th international conference

Event place :

Umea, Sweden

Event date :

from 12 to 16 June 2023

Audience :

International

Main work title :

Words 2023

Editor :

Robert Merças

Anna E. Frid

Publisher :

Springer

ISBN/EAN :

978-3-031-33179-4

Collection name :

Lecture Notes in Computer Science, 13899

Pages :

247-260

Peer reviewed :

Peer reviewed

Funders :

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

Data Set :

https://link.springer.com/chapter/10.1007/978-3-031-33180-0_19

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since 11 May 2023

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