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Une généralisation du triangle de Pascal et la suite A007306
Stipulanti, Manon
2016Séminaire compréhensible de l'ULg
 

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Keywords :
Binomial coefficients; Pascal triangle; Words
Abstract :
[en] We introduce a generalization of Pascal triangle based on binomial coefficients of finite words. These coefficients count the number of times a word appears as a subsequence of another finite word. Similarly to the Sierpinski 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. We consider a sequence (S(n))n≥0 counting the number of positive entries on each row of the generalized Pascal triangle. By introducing a convenient tree structure, we provide a recurrence relation for (S(n))n≥0, we prove that the sequence is 2-regular, give a linear representation and make the connection with the sequence of denominators occurring in the Farey tree.
Disciplines :
Mathematics
Author, co-author :
Stipulanti, Manon  ;  Université de Liège > Département de mathématique > Mathématiques discrètes
Language :
French
Title :
Une généralisation du triangle de Pascal et la suite A007306
Publication date :
25 March 2016
Number of pages :
48
Event name :
Séminaire compréhensible de l'ULg
Event organizer :
ULg - Université de Liège
Event place :
Liège, Belgium
Event date :
25 mars 2016
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 17 May 2016

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