# Article

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Keywords:
combinatorics on words; generalized Thue-Morse word; factor frequency
Summary:
We describe factor frequencies of the generalized Thue-Morse word ${\mathbf t}_{b,m}$ defined for $b \ge 2,$ $m \ge 1,$ $b,m \in \mathbb N$, as the fixed point starting in $0$ of the morphism $$\varphi_{b,m}(k)=k(k+1)\dots(k+b-1),$$ where $k \in \{0,1,\dots, m-1\}$ 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].
References:
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[6] Starosta, Š.: Generalized Thue-Morse words and palindromic richness. Kybernetika 48 (2012), 3, 361–370.

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