Behavior of Digital Sequences Through Exotic Numeration Systems

Julien Leroy, Michel Rigo, Manon Stipulanti

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.


Keywords


Binomial coefficients of words; k-Regular sequences; Summatory functions

Full Text: PDF