Factor frequencies in generalized Thue-Morse words

Ľubomíra Balková

Kybernetika (2012)

  • Volume: 48, Issue: 3, page 371-385
  • ISSN: 0023-5954

Abstract

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We describe factor frequencies of the generalized Thue-Morse word 𝐭 b , m defined for b ≥ 2 , m ≥ 1 , b , m ∈ ℕ , as the fixed point starting in 0 of the morphism ϕ b , 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].

How to cite

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Balková, Ľubomíra. "Factor frequencies in generalized Thue-Morse words." Kybernetika 48.3 (2012): 371-385. <http://eudml.org/doc/246853>.

@article{Balková2012,
abstract = {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 \lbrace 0,1,\dots , m-1\rbrace $ 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].},
author = {Balková, Ľubomíra},
journal = {Kybernetika},
keywords = {combinatorics on words; generalized Thue-Morse word; factor frequency; combinatorics on words; generalized Thue-Morse word; factor frequency},
language = {eng},
number = {3},
pages = {371-385},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Factor frequencies in generalized Thue-Morse words},
url = {http://eudml.org/doc/246853},
volume = {48},
year = {2012},
}

TY - JOUR
AU - Balková, Ľubomíra
TI - Factor frequencies in generalized Thue-Morse words
JO - Kybernetika
PY - 2012
PB - Institute of Information Theory and Automation AS CR
VL - 48
IS - 3
SP - 371
EP - 385
AB - 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 \lbrace 0,1,\dots , m-1\rbrace $ 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].
LA - eng
KW - combinatorics on words; generalized Thue-Morse word; factor frequency; combinatorics on words; generalized Thue-Morse word; factor frequency
UR - http://eudml.org/doc/246853
ER -

References

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  1. Allouche, J.-P., Shallit, J., Sums of digits, overlaps, and palindromes, Discrete Math. Theoret. Comput. Sci. 4 (2000), 1–10. Zbl1013.11004MR1755723
  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. Zbl0790.11017MR1287223
  4. Frid, A., On the frequency of factors in a D0L word, J. Automata, Languages and Combinatorics 3 (1998), 29–41. Zbl0912.68116MR1663865
  5. Queffélec, M., Substitution dynamical systems – Spectral analysis, Lecture Notes in Math. 1294 (1987). Zbl1225.11001
  6. Starosta, Š., Generalized Thue-Morse words and palindromic richness, Kybernetika 48 (2012), 3, 361–370. 

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