Mignosi, Filippo On the number of factors of Sturmian words. (English) Zbl 0728.68093 Theor. Comput. Sci. 82, No. 1, 71-84 (1991). The author presents new results concerning the Sturmian words which were conjectured some years ago. The author gives and proves an exact estimation of the size of \(A_ m\) (the set of factors of length m of all the Sturmian words). He also gives a combinatorial version of the Riemann hypothesis. Reviewer: P.-G.Holban (Iaşi) Cited in 3 ReviewsCited in 53 Documents MSC: 68R15 Combinatorics on words Keywords:factors of Sturmian words; Riemann hypothesis PDF BibTeX XML Cite \textit{F. Mignosi}, Theor. Comput. Sci. 82, No. 1, 71--84 (1991; Zbl 0728.68093) Full Text: DOI OpenURL References: [1] Berstel, J., Trace de droites, fractions continues et morphismes itérés, () [2] also Theoret. Comput. Sci., to appear · Zbl 0694.68048 [3] Chomsky, N.; Schützenberger, M.P., The algebraic theory of context-free languages, (), 118-161 · Zbl 0148.00804 [4] Cobham, A., Uniform tag sequences, Math. systems theory, 6, 2, 164-192, (1972) · Zbl 0253.02029 [5] Coven, E.M.; Hedlund, G.A., Sequences with minimal block growth, Math. systems theory, 7, 2, 138-153, (1973) · Zbl 0256.54028 [6] Flajolet, P., Ambiguity and transcendence, (), 179-188 [7] Franel, J., LES suites de Farey et le probléme des nombres premiers, Göttinger nachrichten, 198-201, (1924) · JFM 50.0119.01 [8] Hardy, G.H.; Wright, E.M., An introduction to the theory of numbers, (1983), Oxford Univ. Press · Zbl 0020.29201 [9] F. Mignosi, Infinite words with linear subword complexity, Theoret. Comput. Sci., to appear. · Zbl 0682.68083 [10] Morse, M.; Hedlund, G.A., Symbolic dynamics II: Sturmian trajectories, Amer. J. math., 62, 1-42, (1940) · JFM 66.0188.03 [11] G. Rauzy, Suites á termes dans un alphabet fini, in: Séminaire de Théorie des Nombres de Bordeaux, Année 1982-1983, Expose No. 25. · Zbl 0547.10048 [12] Rauzy, G., Mots infinis en arithmétique, (), 165-171 · Zbl 0613.10044 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.