Sur les facteurs des suites de sturm

Abstract

In this paper, we study a construction which connects to each line with slope p/ q (such that gcd( p, q) = 1 and q⩽ n) a word of length n over the alphabet {0, 1}. We show that this construction yields the language of all the factors of the sturmian sequences. We first obtain a functional equation whose solution is the generating function of this language, and then we give a conjecture relating this generating function to the Euler function.