Three distance theorems and combinatorics on words
This paper is first a very nice survey on the three distance theorem [see \textit{V. Turán-Sos}, Ann. Univ. Sci. Budapest. Rolando Eötvös, Sect. Math. 1, 127-134 (1958; Zbl 0094.02903) and \textit{S. Świerczkowski}, Fundam. Math. 46, 187-189 (1959; Zbl 0085.27203)] and its generalizations, going from codings of rotations to block complexities of sequences over finite alphabets, and from Beatty sequences to Sturmian sequences. It also contains new results on the frequencies of factors for sequences defined as codings of irrational rotations on \(\mathbb{R}/\mathbb{Z}\). A large bibliography of 58 items is given. Note that the following papers have appeared: [4] \textit{V. Berthé} and \textit{L. Vuillon}, Tilings and rotations on the torus: a two-dimensional generalization of Sturmian sequences, Discrete Math. 223, 27-53 (2000; Zbl 0970.68124). [5] J. Anal. Math. 79, 1-31 (1999; Zbl 0996.37006). [12] Theor. Comput. Sci. 230, 97-116 (2000; Zbl 0947.68543). [13] J. Théor Nombres Bordx. 13, 371-394 (2001; Zbl 1038.37010). [22] Theor. Comput. Sci. 215, 31-49 (1999; Zbl 0913.68163). [23] Acta Arith. 85, 157-177 (1998; Zbl 0910.11007). [36] SCAN-98 Conference (see Zbl 0949.65013). [48] Acta Arith. 97, 195-210 (2001; Zbl 1004.11040.
scientific article; zbMATH DE number 1558719