Hubert, P. Well-balanced sequences. (Suites équilibrées.) (French) Zbl 0944.68149 Theor. Comput. Sci. 242, No. 1-2, 91-108 (2000). Summary: Well-balanced sequences are one of the possible generalizations of sturmian sequences. We give a combinatoric and geometric interpretation of non-periodic well-balanced sequences. We compute the complexity of these sequences for integers large enough. Cited in 2 ReviewsCited in 38 Documents MSC: 68R15 Combinatorics on words 11B85 Automata sequences Keywords:non-periodic well-balanced sequences; generalizations of Sturmian sequences; complexity × Cite Format Result Cite Review PDF Full Text: DOI References: [1] P. Alessandri, V. Berthé, Three distances theorems and combinatorics on words, preprint.; P. Alessandri, V. Berthé, Three distances theorems and combinatorics on words, preprint. · Zbl 0997.11051 [2] Arnoux, P.; Rauzy, G., Représentation géométrique de suites de complexité \(2n+1\), Bull. SMF, 119, 101-117 (1991) · Zbl 0789.28011 [3] Berstel, J.; Pocciola, M., A geometric proof of the enumeration formula for Sturmian words, Inform. J. Algebra Comput., 3, 349-355 (1993) · Zbl 0802.68099 [4] Corfeld, I. P.; Formin, S. V.; G. Sinai, Ya., Ergodic Theory (1982), Springer: Springer Berlin · Zbl 0493.28007 [5] Coven, E. M.; Hedlund, G. A., Sequences with minimal block growth, Math. Systems Theory, 7, 2 (1973) · Zbl 0256.54028 [6] Duluc, S.; Gouyou-Beauchamps, D., Sur les facteurs des suites de sturm, Theoret. Comput. Sci., 71, 381-400 (1990) · Zbl 0694.68048 [7] Fezenczi, S., Bounded remainder sets, Acta Arithmetica LXI., 4, 319-326 (1992) · Zbl 0774.11037 [8] Hedlund, G. A.; Morse, M., Symbolic dynamics II. sturmian trajectories, Amer. J. Math., 62 (1940) · JFM 66.0188.03 [9] L. Graham, R., Covering the Positive Integers by disjoints sets of the form \({[n α + β] :n=1,2,… }\), J. Combin. Theory Ser, A15, 354-358 (1973) · Zbl 0279.10042 [10] de Luca, A.; Mignosi, F., Some combinatorial properties of Sturmian words, Theoret. Comput. Sci., 136, 361-385 (1994) · Zbl 0874.68245 [11] Mignosi, F., On the number of factors of Sturmian words, Theoret. Comput. Sci., 82, 71-84 (1991) · Zbl 0728.68093 [12] G. Rauzy, Ensembles à restes bornés, Séminaire de théorie des nombres de Bordeaux, Exposé 24, 1983-1984.; G. Rauzy, Ensembles à restes bornés, Séminaire de théorie des nombres de Bordeaux, Exposé 24, 1983-1984. · Zbl 0547.10044 [13] G. Rauzy, Mots infinis en arithmétique, Automata on Infinite Words, Lecture Notes in Computer Science, vol. 192, Springer, Berlin, 1985, pp. 165-171.; G. Rauzy, Mots infinis en arithmétique, Automata on Infinite Words, Lecture Notes in Computer Science, vol. 192, Springer, Berlin, 1985, pp. 165-171. · Zbl 0613.10044 [14] Séébold, P., Fibonacci morphisms and sturmian words, Theoret. Comput. Sci., 88, 367-384 (1991) · Zbl 0737.68068 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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.