[en] Combinatorics on words is a relatively new domain of discrete mathematics, which focuses on the study of words and formal languages. In this context, a finite word is simply a finite sequence of letters, or symbols, that belong to a finite set called the alphabet. For instance, 01101 and 01 are two finite (binary) words over the binary alphabet {0, 1}. The binomial coefficient (u,v) of two finite words u and v is the number of occurrences of v as a v subsequence of u. For example, (01101,01) = 4. This concept, which is a natural generalization of the classical binomial coefficients of nonnegative integers, has been widely studied for the last thirty years or so. In this talk, I will first recall the link between the classical Pascal triangle and the Sierpiński gasket, and then present a way of extending both objects to binomial coefficients of (binary) words.
Disciplines :
Mathematics
Author, co-author :
Stipulanti, Manon ; Université de Liège - ULiège > Département de mathématique > Mathématiques discrètes
Language :
English
Title :
A way of extending Pascal and Sierpinski triangles to finite words
Publication date :
24 September 2018
Number of pages :
77
Event name :
Young Mathematicians Symposium of the Greater Region
Event organizer :
Université de Lorraine
Event place :
Nancy, France
Event date :
du 24 au 25 septembre 2018
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@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).