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2000 | 95 | 2 | 167-184
Tytuł artykułu

A generalization of Sturmian sequences: Combinatorial structure and transcendence

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
Słowa kluczowe
Czasopismo
Rocznik
Tom
95
Numer
2
Strony
167-184
Opis fizyczny
Daty
wydano
2000
otrzymano
1998-12-23
poprawiono
1999-05-24
Twórcy
  • Department of Mathematics, University of North Texas, Denton, TX 76203-5116, U.S.A.
  • Department of Mathematics, University of North Texas, Denton, TX 76203-5116, U.S.A.
Bibliografia
  • [1] J.-P. Allouche and L. Q. Zamboni, Algebraic irrational binary numbers cannot be fixed points of non-trivial constant length or primitive morphisms, J. Number Theory 69 (1998), 119-124.
  • [2] P. Arnoux and S. Ito, Pisot substitutions and Rauzy fractals, preprint, 1999.
  • [3] P. Arnoux et G. Rauzy, Représentation géométrique de suites de complexité $2n+1$, Bull. Soc. Math. France 119 (1991), 199-215.
  • [4] J. Berstel, Mots de Fibonacci, Séminaire d'Informatique Théorique, LITP, Universités Paris 6-7 (1980-1981), 57-78.
  • [5] J. Berstel et P. Séébold, Morphismes de Sturm, Bull. Belg. Math. Soc. 1 (1994), 175-189.
  • [6] V. Berthé, Fréquences des facteurs des suites sturmiennes, Theoret. Comput. Sci. 165 (1996), 295-309.
  • [7] M. G. Castelli, F. Mignosi and A. Restivo, Fine and Wilf's theorem for three periods and a generalization of sturmian words, ibid. 218 (1999), 83-94.
  • [8] N. Chekhova, Les suites d'Arnoux-Rauzy : algorithme d'approximation et propriétés ergodiques, preprint, 1998.
  • [9] N. Chekhova, P. Hubert et A. Messaoudi, Propriétés combinatoires, ergodiques et arithmétiques de la substitution de Tribonacci, J. Théor. Nombres Bordeaux, to appear.
  • [10] E. M. Coven and G. A. Hedlund, Sequences with minimal block growth, Math. Systems Theory 7 (1973), 138-153.
  • [11] A. de Luca and F. Mignosi, Some combinatorial properties of Sturmian words, Theoret. Comput. Sci. 136 (1994), 361-385.
  • [12] F. Durand, A characterization of substitutive sequences using return words, Discrete Math. 179 (1998), 89-101.
  • [13] F. Durand, Linearly recurrent subshifts, Ergod. Theory Dynam. Systems, to appear.
  • [14] F. Durand and B. Host, private communication.
  • [15] F. Durand, B. Host and C. Skau, Substitution dynamical systems, Bratteli diagrams and dimension groups, Ergod. Theory Dynam. Systems 19 (1999), 953-993.
  • [16] S. Ferenczi, Les transformations de Chacon : combinatoire, structure géométrique, lien avec les systèmes de complexité $2n+1$, Bull. Soc. Math. France 123 (1995), 271-292.
  • [17] S. Ferenczi and C. Mauduit, Transcendence of numbers with a low complexity expansion, J. Number Theory 67 (1997), 146-161.
  • [18] C. Holton and L. Q. Zamboni, Descendants of primitive substitutions, Theory Comput. Syst. 32 (1998), 133-157.
  • [19] C. Holton and L. Q. Zamboni, Directed graphs and substitutions, in: From Crystals to Chaos, P. Hubert, R. Lima and S. Vaienti (eds.), World Sci., 1999, to appear.
  • [20] J. H. Loxton and A. van der Poorten, Arithmetic properties of automata: regular sequences, J. Reine Angew. Math. 392 (1988), 57-69.
  • [21] K. Mahler, Lectures on Diophantine Approximations, Part I: $g$-adic Numbers and Roth's Theorem, Univ. of Notre Dame, 1961.
  • [22] K. Mahler, Arithmetische Eigenschaften einer Klasse von Dezimalbrüchen, Proc. Konink. Nederl. Akad. Wetensch. Ser. A 40 (1937), 421-428.
  • [23] F. Mignosi, Infinite words with linear subword complexity, Theoret. Comput. Sci. 65 (1989), 221-242.
  • [24] F. Mignosi, On the number of factors of Sturmian words, ibid. 82 (1991), 71-84.
  • [25] F. Mignosi and G. Pirillo, Repetitions in the Fibonacci infinite word, RAIRO Inform. Théor. Appl. 26 (1992), 199-204.
  • [26] M. Morse and G. A. Hedlund, Symbolic dynamics, Amer. J. Math. 60 (1938), 815-866.
  • [27] M. Morse and G. A. Hedlund, Symbolic dynamics II: Sturmian sequences, ibid. 62 (1940), 1-42.
  • [28] M. Queffélec, Substitution Dynamical Systems-Spectral Analysis, Lecture Notes in Math. 1294, Springer, 1987.
  • [29] G. Rauzy, Mots infinis en arithmétique, in: Automata on Infinite Words, M. Nivat and D. Perrin (eds.), Lecture Notes in Comput. Sci. 192, Springer, Berlin, 1985, 165-171.
  • [30] G. Rauzy, Nombres algébriques et substitutions, Bull. Soc. Math. France 110 (1982), 147-178.
  • [31] G. Rote, Sequences with subword complexity $2n$, J. Number Theory 46 (1994), 196-213.
  • [32] J.-I. Tamura, A class of transcendental numbers having explicit $g$-adic and Jacobi-Perron expansions of arbitrary dimension, Acta Arith. 71 (1995), 301-329.
  • [33] N. Wozny and L. Q. Zamboni, Frequencies of factors in Arnoux-Rauzy sequences, Acta Arith., to appear.
  • [34] L. Q. Zamboni, Une généralisation du théorème de Lagrange sur le développement en fraction continue, C. R. Acad. Sci. Paris Sér. I, 327 (1998), 527-530.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-aav95z2p167bwm
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