FACTOR FREQUENCIES IN GENERALIZED THUE-MORSE WORDS

We describe factor frequencies of the generalized Thue-Morse word t(b,m) defined for b >= 2, m >= 1, b, m, is an element of N, as the fixed point starting in 0 of the morphism phi b,m (k) = k (k+ 1) ... (k + b - 1), where k is an element of {0,1, ... ,m - 1} and where the letters are expressed modulo M. We use the result of Frid [4] and the study of generalized Time-Morse words by Starosta [6].