Factor frequencies in generalized Thue-Morse words

L'ubomíra Balková We describe factor frequencies of the generalized Thue–Morse word t b,m defined for b ≥ 2, m ≥ 1, b, m ∈ N, as the fixed point starting in 0 of the morphism ϕ b,m (k) = k(k + 1). .. (k + b − 1), where k ∈ {0, 1,. .. , m − 1} and where the letters are expressed modulo m. We use the result of Frid [4] and the study of generalized Thue–Morse words by Starosta [6].