[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.
Disciplines :
Mathematics
Author, co-author :
Stipulanti, Manon ; Université de Liège > Département de mathématique > Mathématiques discrètes
Language :
French
Title :
Une généralisation du triangle de Pascal
Publication date :
22 March 2016
Number of pages :
60
Event name :
Discrete Math. Seminar
Event organizer :
ULg - Université de Liège
Event place :
Liège, Belgium
Event date :
22 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).
