Geodesic
Factor frequencies in generalized Thue-Morse words
Kybernetika, Tome 48 (2012) no. 3, pp. 371-385

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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].
Classification : 68R15
Keywords: combinatorics on words; generalized Thue-Morse word; factor frequency 
@article{KYB_2012__48_3_a2,
     author = {Balkov\'a, \v{L}ubom{\'\i}ra},
     title = {Factor frequencies in generalized {Thue-Morse} words},
     journal = {Kybernetika},
     pages = {371--385},
     publisher = {mathdoc},
     volume = {48},
     number = {3},
     year = {2012},
     mrnumber = {2975795},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KYB_2012__48_3_a2/}
}
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Balková, Ľubomíra. Factor frequencies in generalized Thue-Morse words. Kybernetika, Tome 48 (2012) no. 3, pp. 371-385. http://geodesic.mathdoc.fr/item/KYB_2012__48_3_a2/