Binomial coefficients; Pascal triangle; Subwords; b-regularity; Asymptotics; Summatory function
Abstract :
[en] We consider the sequence (Sb(n))n≥0 counting the number of distinct (scattered) subwords occurring in the base-b expansion of the non-negative integers. By using a convenient tree structure, we provide recurrence relations for (Sb(n))n≥0 leading to the b-regularity of the latter sequence. Then we deduce the asymptotics of the summatory function of the sequence (Sb(n))n≥0.
Disciplines :
Mathematics
Author, co-author :
Leroy, Julien ; Université de Liège - ULiège > Département de mathématique > Département de mathématique
Rigo, Michel ; Université de Liège - ULiège > Département de mathématique > Mathématiques discrètes
Stipulanti, Manon ; Université de Liège - ULiège > Département de mathématique > Mathématiques discrètes
Language :
English
Title :
Counting Subwords Occurrences in Base-b Expansions
Publication date :
2018
Journal title :
Integers
eISSN :
1553-1732
Publisher :
Integers, Carrollton, United States - Georgia
Special issue title :
Special Volume in Honor of Jeffrey Shallit on the Occasion of His 60th Birthday
