Invertible substitutions and Sturmian sequences

European Journal of Combinatorics - Tập 24 - Trang 983-1002 - 2003
Bo Tan1,2, Zhi-Ying Wen3
1Department of Mathematics, Wuhan University, Wuhan 430072, P. R. China
2Département de Mathématiques, bát. 425, Université de Paris-Sud, 91405 Orsay Cedex, France
3Department of Mathematics, Tsinghua University, Beijing 100084, P.R. China

Tài liệu tham khảo

P. Arnoux, Sturmian sequences, CIMPA Summer School Lectures, 1996

Berstel, 1996, Recent results on Sturmian words, vol. II, 13

V. Berthé, S. Ferenczi, C. Mauduit, A. Siegel (Eds.), Substitutions in Dynamics, Arithmetics and Combinatorics, Institut de Mathématiques de Luminy, Marseille

W.T. Cao, Z.Y. Wen, Some properties of the factors of Sturmian sequences (preprint)

S. Ferenczi, Symbolic Dynamics, CIMPA Summer School Lectures, 1996

Fraenkel, 1978, Determination of ⌊nθ⌋ by its sequence of differences, Canad. Math. Bull., 21, 441, 10.4153/CMB-1978-077-0

Hedlund, 1940, Sturmian sequences, Amer. J. Math., 61, 1

Khintchine, 1963

Lothaire, 1983, Combinatorics on words, vol. 17

Peyrière, 1993, Polynômes associés aux endomorphismes de groupe libres, L’enseignement mathématique, 39, 153

Queffelec, 1987, Substitution Dynamical Systems—Spectral Analysis, vol. 1294

Séébold, 1991, Fibonacci morphisms and Sturmian words, Theoret. Comput. Sci., 88, 367, 10.1016/0304-3975(91)90383-D

Stolarsky, 1976, Beatty sequences, continued fractions, and certain shift operators, Canad. Math. Bull., 19, 473, 10.4153/CMB-1976-071-6

Z.X. Wen, Z.Y. Wen, Some studies of factors of infinite words generated by invertible substitution, 5th Conference on Formal Power Series and Algebraic Combinatorics, Florence, 1993, pp. 455–466

Wen, 1994, Local isomorphisms of invertible substitutions, C. R. Acad. Sci. Paris, t.318, 299

S.-I. Yasutomi, On Sturmian sequences which are invariant under some substitutions, Number Theory and its Applications (Kyoto, 1997), Kluwer Acad. Publ., Dordrecht, pp. 347–373. Dev. Math. 2 (1999)