1. S. Beatty, Problem 3173, Amer. Math. Monthly 33 (1926). p. 159 solutions ibid. 34 (1927). p. 159.

   Article MathSciNet  Google Scholar 

2. L. Carlitz. Fibonacci representations. Fib. Quart. (1968). p. 193–220

   Google Scholar 

3. L. Carlitz, V.L. Hoggatt Jr, R. Scoville, Fibonacci representations. Fib. Quart. 10 (1972). p. 1–28.

   MathSciNet MATH  Google Scholar 

4. E. Coven, G. Hedlund, Sequences with minimal block growth. Math. Syst. Theory 7 (1973). p. 138–153.

   Article MathSciNet MATH  Google Scholar 

5. M. Crochemore, An optimal algorithm for computing repetitions of a word. Inf. Process. Letters 12 (1981), p. 244–250.

   MathSciNet MATH  Google Scholar 

6. K. Culik II. A. Salomaa. Ambiguity and decision problems concerning number systems. Information and Control56. 1984. 139–153.

   Article MathSciNet  Google Scholar 

7. A. de Luca, A combinatorial property of the Fibonacci words. Inf. Process. Letters 12 (1981). p. 193–195.

   Article MATH  Google Scholar 

8. A. de Luca, A. Restivo, Representations of Integers and Language Theory. MFCS. 1984. Lecture Notes Comp. Sciences176. 407–415.

   Google Scholar 

9. S. Eilenberg. “Automata. Languages and Machines”. Academic Press 1974.

   Google Scholar 

10. A.S. Fraenkel. Systems of Numeration. American Math. Monthly, to appear.

    Google Scholar 

11. C. Frougny. On linear Numeration Systems, in preparation.

    Google Scholar 

12. J. Honkala. Bases and ambiguity of number systems. Theoret. Comput. Sci.,31, 1984. 61–71.

    Article MathSciNet MATH  Google Scholar 

13. J. Karhumaki. On cube-free ω-words generated by binary morphisms. Discr. Appl. Math. 5 (1983). p. 279–297.

    Article MathSciNet  Google Scholar 

14. D. Knuth. “The Art of Computer Programming”. Vol. I. Addison Wesley 1968.

    Google Scholar 

15. D. Knuth. J. Morris. V. Pratt. Fast pattern matching in strings. SIAM J. Comput. 6 (1977). p. 323–350.

    Article MathSciNet MATH  Google Scholar 

16. G. Rauzy. Mots infinis en arithmétique, in M. Nivat, D. Perrin (eds), “Automata on infinite words”, Lecture Notes in Computer Science 192. 1985. Springer, p. 165–171.

    Google Scholar 

17. G. Rozenberg. A. Salomaa. “The Mathematical Theory of L Systems”. Academic Press. 1980.

    Google Scholar 

18. J. Sakarovitch. Easy multiplication. Rapport LITP 85–41. to appear.

    Google Scholar 

19. P. Seebold. Propriétés combinatoires des mots infinis engendrés par certains morphismes. Thèse de 3ème cycle. Rapport LITP 85–16.

    Google Scholar 

20. K. B. Stolarsky. Beatty sequences, continued fractions, and certain shift operators. Canad. Math. Bull 19 (1976), p. 473–482.

    Article MathSciNet MATH  Google Scholar 

21. E. Zeckendorf. Représentation des nombres naturels par une somme de nombres de Fibonacci ou de nombres de Lucas. Bull. Soc. Royale des Sciences de Liège. 1972. p. 179–182.

    Google Scholar 

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