Three distance theorems and combinatorics on words
type: Item
instance of: scholarly article
title: Three distance theorems and combinatorics on words
zbMATH Open document ID: 0997.11051
author: Pascal Alessandri
author: Valérie Berthé
published in: L'Enseignement Mathématique. 2e Série
publication date: 2001-01-30T00:00:00Z
review text: 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.
reviewed by: Jean-Paul Allouche
Mathematics Subject Classification ID: 11J71
Mathematics Subject Classification ID: 11K06
Mathematics Subject Classification ID: 11-02
Mathematics Subject Classification ID: 68R15
zbMATH DE Number: 1558719
zbMATH Keywords: frequencies of blocks
zbMATH Keywords: survey
zbMATH Keywords: three distance theorem
zbMATH Keywords: block complexities of sequences
zbMATH Keywords: finite alphabets
zbMATH Keywords: Beatty sequences
zbMATH Keywords: Sturmian sequences
zbMATH Keywords: bibliography
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1558719