[en] The binomial coefficient (u,v) of two finite words u and v (on a finite alphabet) is the number of times the word v appears inside the word u as a subsequence (or, as a "scattered" subword). For instance, (abbabab,ab)=4. This concept naturally extends the classical binomial coefficients of integers, and has been widely studied for about thirty years (see, for instance, Simon and Sakarovitch). In this talk, I present the research lead from October 2015: I give the main ideas that lead to an extension of the Pascal triangles to base-2 expansions of integers and also give an overview of the results obtained so far, linked to this generalization.
Disciplines :
Mathematics
Author, co-author :
Stipulanti, Manon ; Université de Liège - ULiège > Département de mathématique > Mathématiques discrètes
Language :
English
Title :
An extension of the Pascal triangle and the Sierpiński gasket to finite words
Publication date :
15 December 2017
Number of pages :
91
Event name :
Groupe de travail du thème "Combinatoire Énumérative et Algébrique" de l'équipe Combinatoire et Algorithmique du LaBRI
Event organizer :
Laboratoire Bordelais de Recherche en Informatique (LaBRI)
Event place :
Bordeaux, France
Event date :
15 décembre 2017
Audience :
International
Funders :
FRIA - Fonds pour la Formation à la Recherche dans l'Industrie et dans l'Agriculture
Commentary :
Work in collaboration with Julien Leroy (ULg, j.leroy@uliege.be) and Michel Rigo (ULg, m.rigo@uliege.be). // Travail en collaboration avec Julien Leroy (ULg, j.leroy@uliege.be) et Michel Rigo (ULg, m.rigo@uliege.be).
