Paper published in a book (Scientific congresses and symposiums)
Automaticity and Parikh-collinear Morphisms
Rigo, Michel; Stipulanti, Manon; Whiteland, Markus
2023In Robert Merças; Anna E. Frid (Eds.) Words 2023
Peer reviewed
 

Files


Full Text
conf-version.pdf
Publisher postprint (2.58 MB)
Download

All documents in ORBi are protected by a user license.

Send to



Details



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 [BE]
Available on ORBi :
since 11 May 2023

Statistics


Number of views
40 (6 by ULiège)
Number of downloads
62 (2 by ULiège)

Scopus citations®
 
1
Scopus citations®
without self-citations
0

Bibliography


Similar publications



Contact ORBi