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arXiv · 1705.08322

Behavior of digital sequences through exotic numeration systems

Julien Leroy·Michel Rigo·Manon Stipulanti
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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.

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Julien Leroy, Michel Rigo, Manon Stipulanti. 2017-05-23. Behavior of digital sequences through exotic numeration systems. https://arxiv.org/abs/1705.08322

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