Behavior of Digital Sequences Through Exotic Numeration Systems

  • Julien Leroy
  • Michel Rigo
  • Manon Stipulanti
Keywords: Binomial coefficients of words, k-Regular sequences, Summatory functions

Abstract

Many digital functions studied in the literature, e.g., the summatory function of the base-$k$ sum-of-digits function, have a behavior showing some periodic fluctuation. Such functions are usually studied using techniques from analytic number theory or linear algebra. In this paper we develop a method based on exotic numeration systems and we apply it on two examples motivated by the study of generalized Pascal triangles and binomial coefficients of words.

Author Biographies

Julien Leroy, University of Liège
Department of mathematics
Michel Rigo, University of Liège
Department of mathematics
Manon Stipulanti, University of Liège
Department of mathematics
Published
2017-03-03
Article Number
P1.44