On the Number of Unbordered Factors

Abstract

We illustrate a general technique for enumerating factors of k-automatic sequences by proving a conjecture on the number f(n) of unbordered factors of the Thue-Morse sequence. We show that f(n) <= n for n >= 4 and that f(n) = n infinitely often. We also give examples of automatic sequences having exactly 2 unbordered factors of every length.