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The number of factors in a paperfolding sequence

Published online by Cambridge University Press:  17 April 2009

Jean-Paul Allouche
Jean-Paul Allouche
Affiliation:
C.N.R.S. U.R.A 0226, Mathématiques et Informatique 351, cours de la Libération F-33405 Talence, Cedex, France
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Abstract

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We prove that the number of factors of length k in any paperfolding sequence is equal to 4k once k ≥ 7.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 46 , Issue 1 , August 1992 , pp. 23 - 32
Copyright
Copyright © Australian Mathematical Society 1992

References

[1]Allouche, J.-P. and Liardet, P., ‘Generalized Rudin-Shapiro sequences’, Acta. Arith. 60 (1991), 1–27.Google Scholar
[2]Allouche, J.-P. and Shallit, J., ‘Suites à complexité ultimement affine’, Congrès “Themate”, Luminy (1991).Google Scholar
[3]Blanchard, A. and France, M. Mendès, ‘Symétrie et transcendance’, Bull. Sci. Math. 106 (1982), 325–335.Google Scholar
[4]Brlek, S., ‘Enumeration of factors in the Thue-Morse word’, Discrete Appl. Math. 24 (1989), 83–96.Google Scholar
[5]Christol, G., Kamae, T., France, M. Medès and Rauzy, G., ‘Suites algébriques, automates et substitutions’, Bull Soc. Math. France 108 (1980), 401–419.Google Scholar
[6]Cobham, A., ‘Uniform tag sequences’, Math. Systems Theory 6 (1972), 164–192.CrossRefGoogle Scholar
[7]Coven, E.M. and Hedlund, G.A., ‘Sequences with minimal block growth’, Math. Systems Theory 7 (1973), 138–153.CrossRefGoogle Scholar
[8]Dekking, M., France, M. Medès and van der Poorten, A., ‘FOLDS!’, Math. Intelligencer 4 (1982), 130–138; 173–181; 190–195.CrossRefGoogle Scholar
[9]Jacobs, K. and Keane, M., ‘0–1-sequences of Toeplitz type’, Z. Wahrsch. verw. Geb. 13 (1969), 123–131.CrossRefGoogle Scholar
[10]de Luca, A. and Varricchio, S., ‘Some combinatorial properties of the Thue-Morse sequence’, Theoret. Comput. Sci. 63 (1989), 333–348.Google Scholar
[11]France, M. Mendès and van der Poorten, A.J., ‘Arithmetic and analytic properties of paperfolding sequences’, (dedicated to K. Mahler), Bull. Austral. Math. Soc. 24 (1981), 123–131.CrossRefGoogle Scholar
[12]France, M. Mendès and Tenenbaum, G., ‘Dimension des courbes planes, papiers pliés et suites de Rudin-Shapiro’, Bull. Soc. Math. France 109 (1981), 207–215.CrossRefGoogle Scholar
[13]Morse, M. and Hedlund, G.A., ‘Symbolic dynamics’, Amer. J. Math. 60 (1938), 815–866.Google Scholar
[14]Tapsoba, T., Complexité de suites automatiques, Thèse de troisième cycle II (Universitè d'Aix - Marseille, 1987).Google Scholar
[15]Thue, A., ‘Über unendliche Zeichenreihen’, Norske vid. Selsk. Skr., I. Mat. Nat. Kl, Christiana 7 (1906), 1–22.Google Scholar
[16]Thue, A., ‘Über die gegenseitige Lage gleicher Teile gewisser Zeichenreihen’, Vorske vid. Selsk. Skr., I. Mat. Nat. Kl., Christiana 1 (1912), 1–67.Google Scholar