Geodesic
Behavior of digital sequences through exotic numeration systems
Julien Leroy1 ; Michel Rigo1 ; Manon Stipulanti1
1University of Liège
The electronic journal of combinatorics, Tome 24 (2017) no. 1

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Zbl arXiv
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.
DOI : 10.37236/6581
Classification : 11A63, 05A10, 11B85, 41A60
Mots-clés : binomial coefficients of words, \(k\)-regular sequences, summatory functions

Julien Leroy  1   ; Michel Rigo  1   ; Manon Stipulanti  1

1 University of Liège 
Julien Leroy; Michel Rigo; Manon Stipulanti. Behavior of digital sequences through exotic numeration systems. The electronic journal of combinatorics, Tome 24 (2017) no. 1. doi: 10.37236/6581
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     author = {Julien Leroy and Michel Rigo and Manon Stipulanti},
     title = {Behavior of digital sequences through exotic numeration systems},
     journal = {The electronic journal of combinatorics},
     year = {2017},
     volume = {24},
     number = {1},
     doi = {10.37236/6581},
     zbl = {1376.11004},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/6581/}
}
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