[en] We deal with formal inverse (in terms of formal series) of the period-doubling sequence. The sequence of indices at which the period-doubling sequence takes the value 0 (resp., 1) is shown to be not k-regular for any k>1. We give recurrence relations for its formal inverse, then we show that it is 2-automatic, and we also provide an automaton that generates it. We study the sequence of indices at which this formal inverse takes the value 1, and we show that it is not k-regular for any k>1 by connecting it to the characteristic sequence of Fibonacci numbers.
Disciplines :
Mathematics
Author, co-author :
Stipulanti, Manon ; Université de Liège - ULiège > Département de mathématique > Mathématiques discrètes
Language :
English
Title :
The formal inverse of the period-doubling word
Publication date :
12 March 2019
Number of pages :
44
Event name :
Discrete Math. Seminar
Event organizer :
ULiège - Université de Liège
Event place :
Liège, Belgium
Event date :
12 mars 2019
Funders :
FRIA - Fonds pour la Formation à la Recherche dans l'Industrie et dans l'Agriculture [BE]
Commentary :
Work in collaboration with Narad Rampersad (University of Winnipeg, Canada). // Travail en collaboration avec Narad Rampersad (University of Winnipeg, Canada).
