Unpublished conference/Abstract (Scientific congresses and symposiums)
Generalized Pascal triangles for binomial coefficients of finite words
Stipulanti, Manon
2017Aperiodic Patterns in Crystals, Numbers and Symbols
 

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Keywords :
Binomial coefficients; Pascal triangle; Words; k-regularity
Abstract :
[en] We introduce a generalization of Pascal triangle based on binomial coefficients of finite words. These coefficients count the number of times a finite word appears as a subsequence of another finite word. Similarly to the Sierpiński gasket that can be built as the limit set, for the Hausdorff distance, of a convergent sequence of normalized compact blocks extracted from Pascal triangle modulo 2, we describe and study the first properties of the subset of [0, 1] × [0, 1] associated with this extended Pascal triangle modulo a prime p. Then we create a new sequence from this extended Pascal triangle that counts, on each row of this triangle, the number of positive binomial coefficients. We show that this sequence is 2-regular. To extend our work, we construct a Pascal triangle using the Fibonacci representations of all the nonnegative integers and we define the corresponding sequence of which we study the regularity. This regularity is an extension of the classical k-regularity of sequences.
Disciplines :
Mathematics
Author, co-author :
Stipulanti, Manon  ;  Université de Liège > Département de mathématique > Mathématiques discrètes
Language :
English
Title :
Generalized Pascal triangles for binomial coefficients of finite words
Publication date :
19 June 2017
Number of pages :
57
Event name :
Aperiodic Patterns in Crystals, Numbers and Symbols
Event organizer :
Lorentz Center
Event place :
Leiden, Netherlands
Event date :
du 19 juin 2017 au 23 juin 2017
By request :
Yes
Audience :
International
Funders :
FRIA - Fonds pour la Formation à la Recherche dans l'Industrie et dans l'Agriculture [BE]
Commentary :
Work in collaboration with Julien Leroy (ULg, j.leroy@ulg.ac.be) and Michel Rigo (ULg, m.rigo@ulg.ac.be). // Travail en collaboration avec Julien Leroy (ULg, j.leroy@ulg.ac.be) et Michel Rigo (ULg, m.rigo@ulg.ac.be).
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since 16 June 2017

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