## On complementary triples of Sturmian bisequences.(English)Zbl 0862.68085

Summary: A Sturmian bisequence $$S$$ is a subset of $$\mathbb{Z}$$ such that the numbers of elements of $$S$$ in any two intervals of equal lengths differ by at most 1. A complementary triple of bisequences is a set of three bisequences such that every integer belongs to exactly one bisequence. In the paper a question of Loeve is answered by giving a characterization of all complementary triples of Sturmian bisequences.

### MSC:

 68R15 Combinatorics on words 20M05 Free semigroups, generators and relations, word problems

### Keywords:

Sturmian bisequences
Full Text:

### References:

 [1] Berstel, J., Tracé de droites, fractions continues et morphismes itérés, (), 287-309 [2] Coven, E.M.; Hedlund, G.A., Sequences with minimal block growth, Math. systems th., 7, 138-153, (1973) · Zbl 0256.54028 [3] Dulucq, S.; Gouyou-Beauchamps, D., Sur LES facteurs des suites de Sturm, Theor. comp. sci., 7, 381-400, (1990) · Zbl 0694.68048 [4] Gottschalk, W.H.; Hedlund, G.A., Topological dynamics, Amer. math. soc. colloq. publ., 36, (1955) · Zbl 0067.15204 [5] Loeve, J.A., Markov decision chains with partial information, () · Zbl 0826.90120 [6] Morse, M.; Hedlund, G.A., Symbolic dynamics, Amer. J. math., 60, 815-866, (1938) · JFM 64.0798.04 [7] Morse, M.; Hedlund, G.A., Symbolic dynamics II — Sturmian trajectories, Amer. J. math., 62, 1-42, (1940) · JFM 66.0188.03 [8] Séébold, P., Problèmes combinatoires liés à la Génération de mots infinis ayant des facteurs prescrits, () [9] Series, C., The geometry of markoff numbers, Math. intel., 7, 20-29, (1985) · Zbl 0566.10024
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.