Abstract
A necessary and sufficient criterion for the existence and value of the frequency of a letter in a morphic sequence is given. This is done using a certain incidence matrix associated with the morphic sequence. The characterization gives rise to a simple if-and-only-if condition that all letter frequencies exist.
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References
Allouche, J.-P., Shallit, J.: Automatic sequences. In: Theory, applications, generalizations. Cambridge University Press, Cambridge (2003)
Apostol, T.M.: Introduction to the Analytic Number Theory. Springer, Heidelberg (1976)
Dekking, F.M.: On the Thue-Morse measure. Acta Univ. Carolin. Math. Phys. 33, 35–40 (1992)
Frid, A.: On the frequency of factors in a DOL word. J. Autom. Lang. Comb. 3(1), 29–41 (1998)
Gantmacher, F.R.: The theory of matrices, vol. 1, 2. Chelsea Publishing Co., New York (1959)
Michel, P.: Sur les ensembles minimaux engendrés par les substitutions de longueur non constante. Ph. D. Thesis, Université de Rennes (1975)
Michel, P.: Stricte ergodicité d’ensembles minimaux de substitution. In: Conze, J.-P., Keane, M.S. (eds.) Théorie Ergodique: Actes des Journées Ergodiques, Rennes 1973/1974. Lecture Notes in Mathematics, vol. 532, pp. 189–201. Springer, Heidelberg (1976)
Minc, H.: Nonnegative matrices. Wiley-Interscience Series in Discrete Mathematics and Optimization. A Wiley-Interscience Publication. John Wiley & Sons, Inc., New York (1988)
Peter, M.: The asymptotic distribution of elements in automatic sequences. Theoretical Computer Science 301, 285–312 (2003)
Pullman, N.J.: Matrix theory and its applications. In: Pure and Applied Mathematics (Selected topics), vol. 35, Marcel Dekker, Inc., New York (1976)
Queffélec, M.: Substitution dynamical systems—spectral analysis. Lecture Notes in Mathematics, vol. 1294. Springer, Berlin (1987)
Saari, K.: On the Frequency of Letters in Pure Binary Morphic Sequences. Developments in language theory, 397–408 (2005)
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Saari, K. (2006). On the Frequency of Letters in Morphic Sequences. In: Grigoriev, D., Harrison, J., Hirsch, E.A. (eds) Computer Science – Theory and Applications. CSR 2006. Lecture Notes in Computer Science, vol 3967. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11753728_34
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DOI: https://doi.org/10.1007/11753728_34
Publisher Name: Springer, Berlin, Heidelberg
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