Behavior of Digital Sequences Through Exotic Numeration Systems

Julien Leroy, Michel Rigo, Manon Stipulanti


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.


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

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