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Recent results on extensions of Sturmian words. (English) Zbl 1007.68141

Summary: Sturmian words are infinite words over a two-letter alphabet that admit a great number of equivalent definitions. Most of them have been given in the past ten years. Among several extensions of Sturmian words to larger alphabets, the Arnoux-Rauzy words appear to share many of the properties of Sturmian words. In this survey, combinatorial properties of these two families are considered and compared.

MSC:

68R15 Combinatorics on words
11B85 Automata sequences
37B10 Symbolic dynamics
68Q45 Formal languages and automata

Keywords:

Sturmian words
Full Text: DOI

References:

[1] Arnoux P., Bull. Belg. Math. Soc. Simon Sterin 8 pp 181– (2001)
[2] Arnoux P., Bull. Soc. Math. France 119 pp 199– (1991)
[3] Berstel J., World Scientific pp 13– (1996)
[4] DOI: 10.1016/0304-3975(95)00224-3 · Zbl 0872.11018 · doi:10.1016/0304-3975(95)00224-3
[5] DOI: 10.1090/S0894-0347-01-00378-2 · Zbl 1057.49007 · doi:10.1090/S0894-0347-01-00378-2
[6] DOI: 10.1016/0166-218X(92)90274-E · Zbl 0683.20045 · doi:10.1016/0166-218X(92)90274-E
[7] DOI: 10.4153/CMB-1993-003-6 · Zbl 0804.11021 · doi:10.4153/CMB-1993-003-6
[8] DOI: 10.1017/S0305004100072236 · Zbl 0823.58012 · doi:10.1017/S0305004100072236
[9] DOI: 10.5802/aif.1792 · Zbl 1004.37008 · doi:10.5802/aif.1792
[10] DOI: 10.1016/S0304-3975(98)00251-5 · Zbl 0916.68114 · doi:10.1016/S0304-3975(98)00251-5
[11] DOI: 10.1007/BF01780584 · Zbl 0299.54032 · doi:10.1007/BF01780584
[12] DOI: 10.1007/BF01762232 · Zbl 0256.54028 · doi:10.1007/BF01762232
[13] DOI: 10.5802/jtnb.83 · Zbl 0786.11041 · doi:10.5802/jtnb.83
[14] DOI: 10.1016/S0304-3975(96)00310-6 · Zbl 0911.68098 · doi:10.1016/S0304-3975(96)00310-6
[15] DOI: 10.1016/0304-3975(94)00035-H · Zbl 0874.68245 · doi:10.1016/0304-3975(94)00035-H
[16] DOI: 10.1016/0020-0190(88)90214-1 · Zbl 0746.68067 · doi:10.1016/0020-0190(88)90214-1
[17] A, Theoret. Comput. Sci. 63 pp 335– (1989)
[18] DOI: 10.1016/S0304-3975(99)00320-5 · Zbl 0981.68126 · doi:10.1016/S0304-3975(99)00320-5
[19] DOI: 10.1016/S0304-3975(97)00188-6 · Zbl 0930.68116 · doi:10.1016/S0304-3975(97)00188-6
[20] DOI: 10.1016/S0012-365X(97)00029-0 · Zbl 0895.68087 · doi:10.1016/S0012-365X(97)00029-0
[21] Ferenczi S., Bull. Soc. Math. France 123 pp 271– (1995)
[22] DOI: 10.1090/S0002-9939-1965-0174934-9 · doi:10.1090/S0002-9939-1965-0174934-9
[23] Holton C., Bull. Soc. Math. France 126 pp 149– (1998) · Zbl 0931.11004 · doi:10.24033/bsmf.2324
[24] DOI: 10.1007/BF03167147 · Zbl 0734.28010 · doi:10.1007/BF03167147
[25] DOI: 10.1051/ita:2000122 · Zbl 0987.68056 · doi:10.1051/ita:2000122
[26] Justin J., Theoret. Inf. Appl. 31 pp 271– (1997)
[27] DOI: 10.1051/ita:2000121 · Zbl 0987.68055 · doi:10.1051/ita:2000121
[28] DOI: 10.5802/jtnb.223 · Zbl 0918.11048 · doi:10.5802/jtnb.223
[29] DOI: 10.2307/2371431 · Zbl 0022.34003 · doi:10.2307/2371431
[30] DOI: 10.5802/jtnb.207 · Zbl 0904.11008 · doi:10.5802/jtnb.207
[31] Rauzy G., Exposé No 25 pp 1–
[32] DOI: 10.1007/3-540-15641-0_32 · doi:10.1007/3-540-15641-0_32
[33] Risley R., Acta Arith. 95 pp 167– (2000)
[34] DOI: 10.1016/S0019-3577(99)80010-X · Zbl 1027.11018 · doi:10.1016/S0019-3577(99)80010-X
[35] DOI: 10.1006/eujc.2000.0444 · Zbl 0968.68124 · doi:10.1006/eujc.2000.0444
[36] DOI: 10.4064/aa96-3-6 · Zbl 0973.11030 · doi:10.4064/aa96-3-6
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