How many square occurrences must a binary sequence contain
Résumé
Every binary word with at least four letters contains a square. Fraenkel and Simpson FraenkelSimpson95 showed that three distinct squares are necessary and sufficient to construct an infinite binary word. We study the following complementary question: how many square occurrences must a binary word contain? We show that this quantity is, in the limit, a constant fraction of the word length, and we give a good estimation of this constant.