Arithmetic subsequences in morphic words

par Olga Parshina (iCJ)

mardi 16 mai 2017, 10:45 → 11:45 Europe/Paris

Bât. Braconnier, salle Fokko du Cloux (ICJ, Université Lyon 1)

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.