About frequencies of letters in generalized automatic sequences. (English) Zbl 1162.68032
Summary: We present some asymptotic results about the frequency of a letter appearing in a generalized unidimensional automatic sequence. Next, we study multidimensional generalized automatic sequences and the corresponding frequencies.
MSC:
| 68R15 | Combinatorics on words |
References:
| [1] | Allouche, J.-P.; Shallit, J., Automatic Sequences, Theory, Applications, Generalizations (2003), Cambridge University Press: Cambridge University Press Cambridge · Zbl 1086.11015 |
| [2] | Cobham, A., Uniform tag sequences, Math. Syst. Theory, 6, 164-192 (1972) · Zbl 0253.02029 |
| [3] | Eilenberg, S., Automata, Languages and Machines, vol. A (1974), Academic Press: Academic Press New York · Zbl 0317.94045 |
| [4] | Fogg, N. P., (Berthé, V.; Ferenczi, S.; Mauduit, C.; Siegel, A., Substitutions in Dynamics, Arithmetics and Combinatorics. Substitutions in Dynamics, Arithmetics and Combinatorics, Lect. Notes in Math., vol. 1794 (2002), Springer-Verlag: Springer-Verlag Berlin) · Zbl 1014.11015 |
| [5] | Gantmacher, F. R., The Theory of Matrices, vol. 2 (1959), Chelsea Publishing Company: Chelsea Publishing Company New York · Zbl 0085.01001 |
| [6] | Grabner, P. J.; Rigo, M., Additive functions with respect to numeration systems on regular languages, Monatsh. Math., 139, 205-219 (2003) · Zbl 1125.11008 |
| [7] | Lecomte, P.; Rigo, M., Numeration systems on a regular language, Theory Comput. Syst., 34, 27-44 (2001) · Zbl 0969.68095 |
| [8] | Lecomte, P.; Rigo, M., On the representation of real numbers using regular languages, Theory Comput. Syst., 35, 13-38 (2002) · Zbl 0993.68050 |
| [9] | Lind, D.; Marcus, B., An Introduction to Symbolic Dynamics and Coding (1995), Cambridge University Press: Cambridge University Press Cambridge · Zbl 1106.37301 |
| [10] | Peter, M., The asymptotic distribution of elements in automatic sequences, Theoret. Comput. Sci., 301, 285-312 (2003) · Zbl 1028.68081 |
| [11] | Peyrière, J., Fréquence des motifs dans les suites doubles invariantes par une substitution, Ann. Sci. Math. Québec, 11, 133-138 (1987) · Zbl 0641.10042 |
| [12] | Rigo, M., Generalization of automatic sequences for numeration systems on a regular language, Theoret. Comput. Sci., 244, 271-281 (2000) · Zbl 0945.68105 |
| [13] | Rigo, M.; Maes, A., More on generalized automatic sequences, J. Autom. Lang. Comb., 7, 351-376 (2002) · Zbl 1033.68069 |
| [14] | Saari, K., On the frequency of letters in pure binary morphic sequences, (Developments in Language Theory. Developments in Language Theory, Lect. Notes Comput. Sci., vol. 3572 (2005), Springer), 397-408 · Zbl 1132.68462 |
| [15] | O. Salon, Suites automatiques à multi-indices, in: Séminaire de théorie des nombres de Bordeaux, Exp. 4 (1986-1987), 4.01-4.27. Followed by an Appendix by J. Shallit, 4-29A-4-36A; O. Salon, Suites automatiques à multi-indices, in: Séminaire de théorie des nombres de Bordeaux, Exp. 4 (1986-1987), 4.01-4.27. Followed by an Appendix by J. Shallit, 4-29A-4-36A · Zbl 0653.10049 |
| [16] | Yablonski, S., Introduction aux mathématiques discrètes (1983), Mir: Mir Moscow · Zbl 0505.94002 |
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