# Behavior of digital sequences through exotic numeration systems

## TL;DR

This paper introduces a novel method using exotic numeration systems to analyze the behavior of digital functions, demonstrating its application on generalized Pascal triangles and binomial coefficients of words.

## Contribution

The paper develops a new approach based on exotic numeration systems for studying digital functions, expanding analytical tools beyond traditional methods.

## Key findings

- Demonstrates the effectiveness of the method on generalized Pascal triangles
- Analyzes binomial coefficients of words using the new approach
- Provides insights into periodic fluctuations in digital 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.