Geodesic
Factor frequencies in generalized Thue-Morse words
Kybernetika, Tome 48 (2012) no. 3, pp. 371-385 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

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].
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},
     year = {2012},
     volume = {48},
     number = {3},
     mrnumber = {2975795},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KYB_2012_48_3_a2/}
}
TY  - JOUR
AU  - Balková, Ľubomíra
TI  - Factor frequencies in generalized Thue-Morse words
JO  - Kybernetika
PY  - 2012
SP  - 371
EP  - 385
VL  - 48
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/KYB_2012_48_3_a2/
LA  - en
ID  - KYB_2012_48_3_a2
ER  - 
%0 Journal Article
%A Balková, Ľubomíra
%T Factor frequencies in generalized Thue-Morse words
%J Kybernetika
%D 2012
%P 371-385
%V 48
%N 3
%U http://geodesic.mathdoc.fr/item/KYB_2012_48_3_a2/
%G en
%F KYB_2012_48_3_a2
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/

[1] Allouche, J.-P., Shallit, J.: Sums of digits, overlaps, and palindromes. Discrete Math. Theoret. Comput. Sci. 4 (2000), 1–10. | MR | Zbl

[2] Balková, L.: Factor frequencies in languages invariant under symmetries preserving factor frequencies. Integers – Electronic Journal of Combinatorial Number Theory 12 (2012), A36.

[3] Dekking, M.: On the Thue-Morse measure. Acta Univ. Carolin. Math. Phys. 33 (1992), 35–40. | MR | Zbl

[4] Frid, A.: On the frequency of factors in a D0L word. J. Automata, Languages and Combinatorics 3 (1998), 29–41. | MR | Zbl

[5] Queffélec, M.: Substitution dynamical systems – Spectral analysis. Lecture Notes in Math. 1294 (1987). | Zbl

[6] Starosta, Š.: Generalized Thue-Morse words and palindromic richness. Kybernetika 48 (2012), 3, 361–370.