[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. After that, I extend the work to any Parry-Bertrand numeration system including the Fibonacci numeration system.
Disciplines :
Mathematics
Author, co-author :
Stipulanti, Manon ; Université de Liège - ULiège > Département de mathématique > Mathématiques discrètes
Language :
English
Title :
Some generalizations of the Pascal triangle: base 2 and beyond
Publication date :
27 April 2018
Number of pages :
77
Event name :
Séminaire de combinatoire et d'informatique mathématique
Event organizer :
Laboratoire de combinatoire et d'informatique mathématique de l'Université du Québec à Montréal
Event place :
Montréal, Canada
Event date :
27 avril 2018
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@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).