Kybernetika 48 no. 3, 371-385, 2012

Factor frequencies in generalized Thue-Morse words

Ľubomíra Balková


We describe factor frequencies of the generalized Thue-Morse word ${\mathbf t}_{b,m}$ defined for $b \geq 2,$ $m\geq 1,$ $b,m \in \mathbb N$, 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].


combinatorics on words, generalized Thue-Morse word, factor frequency




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