Bât. Braconnier, salle Fokko du Cloux (ICJ, Université Lyon 1)
Bât. Braconnier, salle Fokko du Cloux
ICJ, Université Lyon 1
Description
The talk is going to highlight some problems and results related to
studying arithmetic subsequences in infinite words, more precisely:
Let A be a finite alphabet and w=w_0w_1w_2… be an infinite word over this
alphabet. The arithmetic subsequence (or arithmetic factor) of length k, difference d and starting number c is the word consisting of symbols of w with indices c, c+d, c+2d,…, c+(k-1)d. Given a word w, there are several questions to ask: What is the cardinality of the set of arithmetic factors of length k in w ? How do such sets look like? E.g. are there words with period 1 in these sets for every k (words of the form a^k)? How does the cardinality above grow when k tends to infinity? Does the word w contain infinite arithmetic subsequences with period 1?
In studying these questions, we are interested in words which are fixed
points of morphisms. I am going to present the known results and the problems
we are studying.