| Title:
|
Factor frequencies in generalized Thue-Morse words (English) |
| Author:
|
Balková, Ľubomíra |
| Language:
|
English |
| Journal:
|
Kybernetika |
| ISSN:
|
0023-5954 |
| Volume:
|
48 |
| Issue:
|
3 |
| Year:
|
2012 |
| Pages:
|
371-385 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| 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]. (English) |
| Keyword:
|
combinatorics on words |
| Keyword:
|
generalized Thue-Morse word |
| Keyword:
|
factor frequency |
| MSC:
|
68R15 |
| idMR:
|
MR2975795 |
| . |
| Date available:
|
2012-08-31T15:47:41Z |
| Last updated:
|
2013-09-24 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/142944 |
| . |
| Reference:
|
[1] Allouche, J.-P., Shallit, J.: Sums of digits, overlaps, and palindromes.Discrete Math. Theoret. Comput. Sci. 4 (2000), 1–10. Zbl 1013.11004, MR 1755723 |
| Reference:
|
[2] Balková, L.: Factor frequencies in languages invariant under symmetries preserving factor frequencies.Integers – Electronic Journal of Combinatorial Number Theory 12 (2012), A36. |
| Reference:
|
[3] Dekking, M.: On the Thue-Morse measure.Acta Univ. Carolin. Math. Phys. 33 (1992), 35–40. Zbl 0790.11017, MR 1287223 |
| Reference:
|
[4] Frid, A.: On the frequency of factors in a D0L word.J. Automata, Languages and Combinatorics 3 (1998), 29–41. Zbl 0912.68116, MR 1663865 |
| Reference:
|
[5] Queffélec, M.: Substitution dynamical systems – Spectral analysis.Lecture Notes in Math. 1294 (1987). Zbl 1225.11001 |
| Reference:
|
[6] Starosta, Š.: Generalized Thue-Morse words and palindromic richness.Kybernetika 48 (2012), 3, 361–370. |
| . |
