Beta-integers were defined as a generalization of integers by Alfréd Rényi in 1957 in the course of his study of expansions of real numbers in non-integer bases. Together with mathematicians, crystallographers are also interested in this unusual structure. They have found out that beta-lattices are in particular convenience for the description of quasicrystals and their diffraction images., Ľubomíra Balková., and Obsahuje bibliografii
We describe factor frequencies of the generalized Thue-Morse word tb,m defined for b≥2, m≥1, b,m∈N, as the fixed point starting in 0 of the morphism
φb,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].