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All issues Volume 57 (2023) RAIRO-Theor. Inf. Appl., 57 (2023) 12 References
Open Access
Issue
RAIRO-Theor. Inf. Appl.
Volume 57, 2023
Article Number 12
Number of page(s) 23
DOI https://doi.org/10.1051/ita/2023007
Published online 18 December 2023
  1. C. Ahlbach, J. Usatine, C. Frougny and N. Pippenger, Efficient algorithms for Zeckendorf arithmetic. Fibonacci Quart. 51 (2013) 249–255. [MathSciNet] [Google Scholar]
  2. J. Berstel, Fibonacci words – a survey, in The Book of L. (1986) 13–27. [CrossRef] [Google Scholar]
  3. V. Berthé and M. Rigo (Eds.), Combinatorics, Automata and Number Theory, Vol. 135 of Encyclopedia of Mathematics and its Applications. Cambridge University Press, Cambridge (2010). [Google Scholar]
  4. M.W. Bunder, Zeckendorf representations using negative Fibonacci numbers. Fibonacci Quart. 30 (1992) 111–115. [MathSciNet] [Google Scholar]
  5. L. Carlitz, Fibonacci representations. Fibonacci Quart. 6 (1968) 193–220. [MathSciNet] [Google Scholar]
  6. D.E. Daykin, Representation of natural numbers as sums of generalised Fibonacci numbers. J. London Math. Soc. 35 (1960) 143–160. [CrossRef] [Google Scholar]
  7. L.E. Dickson, History of the Theory of Numbers. Vol. I of Divisibility and primality. Chelsea Publishing Co., New York (1966). [Google Scholar]
  8. A.S. Fraenkel, Systems of numeration. Amer. Math. Monthly 92 (1985) 105–114. [Google Scholar]
  9. C. Frougny, Linear numeration systems of order two. Inform. Comput. 77 (1988) 233–259. [Google Scholar]
  10. C. Frougny, Fibonacci representations and finite automata. IEEE Trans. Inform. Theory 37 (1991) 393–399. [Google Scholar]
  11. C. Frougny, On-line finite automata for addition in some numeration systems. Theor. Inform. Appl. 33 (1999) 79–101. [CrossRef] [EDP Sciences] [MathSciNet] [Google Scholar]
  12. C. Frougny and B. Solomyak, On representation of integers in linear numeration systems, in Ergodic Theory of Zd Actions (Warwick, 1993–1994), Vol. 228 of London Math. Soc. Lecture Note Ser. Cambridge University Press, Cambridge (1996) 345–368. [Google Scholar]
  13. C. Frougny and J. Sakarovitch, Number representation and finite automata, in Combinatorics, Automata and Number Theory, Vol. 135 of Encyclopedia Math. Appl. Cambridge University Press, Cambridge (2010) 34–107. [Google Scholar]
  14. R.L. Graham, D.E. Knuth and O. Patashnik, Concrete mathematics, 2nd edn. Addison-Wesley Publishing Company, Reading, MA (1994). [Google Scholar]
  15. V.E.J. Hoggatt, Fibonacci and Lucas Numbers. Houghton Mifflin Company IV, Boston (1969) 92. [Google Scholar]
  16. D.E. Knuth, The art of Computer Programming, Vol. 1. Addison-Wesley, Reading, MA (1997). [Google Scholar]
  17. D.E. Knuth, The Art of Computer Programming. Vol. 2. Addison-Wesley, Reading, MA (1998). [Google Scholar]
  18. D.E. Knuth, The art of Computer Programming. Vol. 4A. Combinatorial Algorithms. Part 1. Addison-Wesley, Upper Saddle River, NJ (2011). [Google Scholar]
  19. S. Labbé and J. Lepšová, A numeration system for Fibonacci-like Wang shifts, in Combinatorics on Words, Vol. 12847 of Lecture Notes in Comput. Sci. Springer, Cham (2021) 104–116. [CrossRef] [Google Scholar]
  20. S. Labbé and J. Lepšová, Dumont–Thomas Numeration Systems for ℤ. (2023) arXiv:2302.14481. [Google Scholar]
  21. C.G. Lekkerkerker, Voorstelling van natuurlijke getallen door een som van getallen van Fibonacci. Simon Stevin 29 (1952) 190–195. [MathSciNet] [Google Scholar]
  22. P. Linz, An Introduction to Formal Languages and Automata, 5th edn. Jones & Bartlett Learning, Sudbury, MA (2012). [Google Scholar]
  23. M. Lothaire, Algebraic Combinatorics on Words (Cambridge University Press: Cambridge), 2002 [Google Scholar]
  24. A. Massuir, J. Peltomäki and M. Rigo, Automatic sequences based on Parry or Bertrand numeration systems. Adv. Appl. Math. 108 (2019) 11–30. [CrossRef] [Google Scholar]
  25. H. Mousavi, L. Schaeffer and J. Shallit, Decision algorithms for Fibonacci-automatic words, I: Basic results. RAIRO Theor. Inform. Appl. 50 (2016) 39–66. [CrossRef] [EDP Sciences] [MathSciNet] [Google Scholar]
  26. OEIS Foundation Inc., Entry A003482 in the on-line encyclopedia of integer sequences (2023). [Google Scholar]
  27. A. Ostrowski, Bemerkungen zur Theorie der Diophantischen Approximationen. Abh. Math. Sem. Univ. Hamburg 1 (1922) 77–98. [CrossRef] [MathSciNet] [Google Scholar]
  28. W. Parry, Representations for real numbers. Acta Math. Acad. Sci. Hungar. 15 (1964) 95–105. [CrossRef] [MathSciNet] [Google Scholar]
  29. A. Rényi, Representations for real numbers and their ergodic properties. Acta Math. Acad. Sci. Hungar. 8 (1957) 477–493. [CrossRef] [MathSciNet] [Google Scholar]
  30. J. Sakarovitch, Easy multiplications. I. The realm of Kleene’s theorem. Inform. and Comput. 74 (1987) 173–197. [CrossRef] [MathSciNet] [Google Scholar]
  31. J. Sakarovitch, Elements of Automata Theory. Cambridge University Press, Cambridge (2009). [CrossRef] [Google Scholar]
  32. N.N. Vorobiev, Fibonacci Numbers. Birkhäuser Verlag, Basel (2002). [CrossRef] [Google Scholar]
  33. E. Zeckendorf, Représentation des nombres naturels par une somme de nombres de Fibonacci ou de nombres de Lucas. Bull. Soc. Roy. Sci. Liège 41 (1972) 179–182. [MathSciNet] [Google Scholar]

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