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Combinatorics on Words: Christoffel Words and Repetitions in Words

Combinatorics on Words: Christoffel Words and Repetitions in Words

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BIBLIOGRAPHY 173[Brl1989] S. Brlek. Enumerati<strong>on</strong> of factors <strong>in</strong> the Thue-Morse word. Discrete Appl.Math. 24 (1-3):83–96, 1989. First M<strong>on</strong>treal C<strong>on</strong>ference <strong>on</strong> <str<strong>on</strong>g>Comb<strong>in</strong>atorics</str<strong>on</strong>g> <strong>and</strong>Computer Science, 1987. ↑99[BW1994] M. Burrows <strong>and</strong> D. J. Wheeler. A block-sort<strong>in</strong>g lossless data compressi<strong>on</strong>algorithm. Technical Report 124, 1994. ↑48[Car1921] F. Carls<strong>on</strong>. Über Potenzreihen mit ganzzahligen Koeffizienten. Math. Z.9 (1-2):1–13, 1921. ↑110[Car2006] A. Carpi. On the repetiti<strong>on</strong> threshold for large alphabets. In Mathematicalfoundati<strong>on</strong>s of computer science 2006, pages 226–237. 2006. ↑159[Car2007] A. Carpi. On Dejean’s c<strong>on</strong>jecture over large alphabets. Theoret. Comput.Sci. 385 (1-3):137–151, 2007. ↑159[Cas1957] J. W. S. Cassels. An <strong>in</strong>troducti<strong>on</strong> to Diophant<strong>in</strong>e approximati<strong>on</strong>. CambridgeTracts <strong>in</strong> Mathematics <strong>and</strong> Mathematical Physics, No. 45. CambridgeUniversity Press, New York, 1957. ↑69[CFL1958] K.-T. Chen, R. H. Fox, <strong>and</strong> R. C. Lynd<strong>on</strong>. Free differential calculus,IV. The quotient groups of the lower central series. Ann. of Math. (2) 68:81–95,1958. ↑51[CS1963] N. Chomsky <strong>and</strong> M.-P. Schützenberger. The algebraic theory of c<strong>on</strong>textfreelanguages. In Computer programm<strong>in</strong>g <strong>and</strong> formal systems, pages 118–161.1963. ↑110[Chr1875] E. B. <strong>Christoffel</strong>. Observatio arithmetica. Annali di Matematica 6:145–152, 1875. ↑3, 6, 54[Chr1888] E. B. <strong>Christoffel</strong>. Lehrsätze über arithmetische eigenschaften du irrati<strong>on</strong>nalzahlen.Annali di Matematica Pura ed Applicata, Series II 15:253–276,1888. ↑3[CKMFR1980] G. Christol, T. Kamae, M. Mendès France, <strong>and</strong> G. Rauzy. Suitesalgébriques, automates et substituti<strong>on</strong>s. Bull. Soc. Math. France 108 (4):401–419, 1980. ↑97, 98[Cob1972] A. Cobham. Uniform tag sequences. Math. Systems Theory 6:164–192,1972. ↑94[Coh1972] H. Cohn. Markoff forms <strong>and</strong> primitive words. Math. Ann. 196:8–22, 1972.↑12[CS1966] M. Coudra<strong>in</strong> <strong>and</strong> M.-P. Schützenberger. Une c<strong>on</strong>diti<strong>on</strong> de f<strong>in</strong>itude desm<strong>on</strong>oïdes f<strong>in</strong>iment engendrés. C. R. Acad. Sci. Paris Sér. A-B 262:A1149–A1151, 1966. ↑168[CH1973] E. M. Coven <strong>and</strong> G. A. Hedlund. Sequences with m<strong>in</strong>imal block growth.Math. Systems Theory 7:138–153, 1973. ↑53, 104[Cro1981] M. Crochemore. An optimal algorithm for comput<strong>in</strong>g the repetiti<strong>on</strong>s <strong>in</strong>a word. Inform. Process. Lett. 12 (5):244–250, 1981. ↑136

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