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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 175[Dic1930] L. E. Dicks<strong>on</strong>. Studies <strong>in</strong> the theory of numbers. U. Chicago Press, 1930.Repr<strong>in</strong>ted as Introducti<strong>on</strong> to the theory of numbers, Dover Publicati<strong>on</strong>s (1957).↑68, 69[DB1937] H. L. Dorwart <strong>and</strong> O. E. Brown. The Tarry-Escott Problem. Amer. Math.M<strong>on</strong>thly 44 (10):613–626, 1937. ↑86[DGB1990] S. Dulucq <strong>and</strong> D. Gouyou-Beauchamps. Sur les facteurs des suites deSturm. Theoret. Comput. Sci. 71 (3):381–400, 1990. ↑50[Duv1983] J.-P. Duval. Factoriz<strong>in</strong>g words over an ordered alphabet. J. Algorithms4 (4):363–381, 1983. ↑51[Erd1961] P. Erdős. Some unsolved problems. Magyar Tud. Akad. Mat. Kutató Int.Közl. 6:221–254, 1961. ↑160[Evd1968] A. A. Evdokimov. Str<strong>on</strong>gly asymmetric sequences generated by a f<strong>in</strong>itenumber of symbols. Dokl. Akad. Nauk SSSR 179:1268–1271, 1968. Englishtranslati<strong>on</strong> <strong>in</strong> Soviet Math. Dokl. 9 (1968), 536–539. ↑161[FM1997] S. Ferenczi <strong>and</strong> C. Mauduit. Transcendence of numbers with a low complexityexpansi<strong>on</strong>. J. Number Theory 67 (2):146–161, 1997. ↑169[FS1998] A. S. Fraenkel <strong>and</strong> J. Simps<strong>on</strong>. How many squares can a str<strong>in</strong>g c<strong>on</strong>ta<strong>in</strong>?.J. Comb<strong>in</strong>. Theory Ser. A 82 (1):112–120, 1998. ↑136, 137, 138[Fro1913] F. G. Frobenius. Über die Markoffschen Zahlen. Sitzungsberichte derKöniglich Preussischen Akademie der Wissenschaften, Berl<strong>in</strong>, 1913. Also <strong>in</strong>:Frobenius, F.G., Gesammelte Abh<strong>and</strong>lungen, Spr<strong>in</strong>ger-Verlag, 1968, vol. 3, 598–627, ed. J.-P. Serre. ↑69, 71[Fur1967] H. Furstenberg. Algebraic functi<strong>on</strong>s over f<strong>in</strong>ite fields. J. Algebra 7:271–277, 1967. ↑97[Gau1986] C. F. Gauss. Disquisiti<strong>on</strong>es arithmeticae. Spr<strong>in</strong>ger-Verlag, New York,1986. Translated <strong>and</strong> with a preface by Arthur A. Clarke, revised by WilliamC. Waterhouse, Cornelius Greither <strong>and</strong> A. W. Grootendorst <strong>and</strong> with a prefaceby Waterhouse. ↑68[GR1993] I. M. Gessel <strong>and</strong> C. Reutenauer. Count<strong>in</strong>g permutati<strong>on</strong>s with given cyclestructure <strong>and</strong> descent set. J. Comb<strong>in</strong>. Theory Ser. A 64 (2):189–215, 1993. ↑48[GLS2008] A. Glen, A. Lauve, <strong>and</strong> F. V. Saliola. A note <strong>on</strong> the Markoff c<strong>on</strong>diti<strong>on</strong><strong>and</strong> central words. Inform. Process. Lett. 105 (6):241–244, 2008. ↑74, 79[GV1991] P. Goralčík <strong>and</strong> T. Vanicek. B<strong>in</strong>ary patterns <strong>in</strong> b<strong>in</strong>ary words. Internat.J. Algebra Comput. 1 (3):387–391, 1991. ↑130[GKP1994] R. L. Graham, D. E. Knuth, <strong>and</strong> O. Patashnik. C<strong>on</strong>crete mathematics:a foundati<strong>on</strong> for computer science. Addis<strong>on</strong>-Wesley L<strong>on</strong>gman Publish<strong>in</strong>g Co.,Inc., Bost<strong>on</strong>, MA, USA, 1994. ↑57, 65

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