Open Access
RAIRO-Theor. Inf. Appl.
Volume 57, 2023
Article Number 4
Number of page(s) 22
Published online 31 March 2023
  1. J.-P. Allouche and J.O. Shallit, The ubiquitous Prouhet-Thue-Morse sequence. In C. Ding, T. Helleseth, and H. Niederreiter, editors, Sequences and Their Applications, Proceedings of SETA ’98. Springer-Verlag (1999), pp. 1–16. [Google Scholar]
  2. J.-P. Allouche and J. Shallit, Automatic Sequences: Theory, Applications, Generalizations. Cambridge University Press (2003). [Google Scholar]
  3. H. Alpert, Differences of multiple Fibonacci numbers. INTEGERS 9 (2009) 745–749. [CrossRef] [MathSciNet] [Google Scholar]
  4. J. Berstel, Sur les mots sans carré définis par un morphisme. In H.A. Maurer, editor, Proc. 6th Int’l Conf. on Automata, Languages, and Programming (ICALP), Vol. 71 of Lecture Notes in Computer Science. Springer-Verlag (1979), pp. 16–25. [Google Scholar]
  5. J. Berstel, Mots de Fibonacci. Séminaire d’informatique Théorique, LITP 6-7 (1980–81) 57–78. [Google Scholar]
  6. J. Berstel, Axel Thue’s Papers on Repetitions in Words: a Translation. Number 20 in Publications du Laboratoire de Combinatoire et d’Informatique Mathématique. Université du Québec à Montréal (1995). [Google Scholar]
  7. M.W. Bunder, Zeckendorf representations using negative Fibonacci numbers. Fibonacci Quart. 30 (1992) 111–115. [MathSciNet] [Google Scholar]
  8. J. Du and X. Su, On the existence of solutions for the Frenkel-Kontorova model on quasi-crystals. Electron. Res. Arch. 29 (2021) 4177–4198. [CrossRef] [MathSciNet] [Google Scholar]
  9. V. Grünwald, Intorno all’aritmetica dei sistemi numerici a base negativa con particolare riguardo al sistema numerico a base negativo-decimale per lo studio delle sue analogie coll’aritmetica (decimale). Giornale di Matematiche di Battaglini 23 (1885) 203–221. Errata, p. 367. [Google Scholar]
  10. P. Hajnal, A short note on Zeckendorf type numeration systems with negative digits allowed. Bull. ICA 97 (2023) 54–66. [Google Scholar]
  11. D.E. Knuth, The Art of Computer Programming, Vol. 3: Seminumerical Algorithms. Addison-Wesley, 3rd ed. (1998). [Google Scholar]
  12. S. Labbé and J. Lepšová, A numeration system for Fibonacci-like Wang shifts. In T. Lecroq and S. Puzynina, editors, WORDS 2021, Vol. 12847 of Lecture Notes in Computer Science. Springer-Verlag (2021), pp. 104–116. [Google Scholar]
  13. C.G. Lekkerkerker, Voorstelling van natuurlijke getallen door een som van getallen van Fibonacci. Simon Stevin 29 (1952) 190–195. [MathSciNet] [Google Scholar]
  14. F. Levé and G. Richomme, Quasiperiodic infinite words: some answers. Bull. Eur Assoc. Theor. Comput. Sci. 84 (2004) 128–138. [Google Scholar]
  15. J. Meleshko, P. Ochem, J. Shallit and S.L. Shan, Pseudoperiodic words and a question of Shevelev. Preprint arXiv:2207.10171 (2022). [Google Scholar]
  16. H. Mousavi, Automatic theorem proving in Walnut. Preprint arXiv:1603.06017 (2016). [Google Scholar]
  17. H. Mousavi, L. Schaeffer and J. Shallit, Decision algorithms for Fibonacci-automatic words, I: basic results. RAIRO Inform. Théor. Appl. 50 (2016) 39–66. [CrossRef] [EDP Sciences] [MathSciNet] [Google Scholar]
  18. S.W. Rosema and R. Tijdeman, The Tribonacci substitution. Electronic J. Combinatorics 5 (2005) #A13 (electronic). [Google Scholar]
  19. J. Shallit, Synchronized sequences. In T. Lecroq and S. Puzynina, editors, WORDS 2021. Vol. 12847 of Lecture Notes in Computer Science. Springer-Verlag (2021), pp. 1–19. [Google Scholar]
  20. J. Shallit, The Logical Approach to Automatic Sequences: Exploring Combinatorics on Words with Walnut. Vol. 482 of London Math. Soc. Lecture Notes Series. Cambridge University Press (2022). [Google Scholar]
  21. J. Shallit and A. Shur, Subword complexity and power avoidance. Theoret. Comput. Sci. 792 (2019) 96–116. [CrossRef] [MathSciNet] [Google Scholar]
  22. V. Shevelev, Equations of the form t(x + a) = t(x) and t(x + a) = 1 – t(x) for Thue-Morse sequence. Preprint arXiv:0907.0880 (2012). [Google Scholar]
  23. V. Shevelev, Two analogs of the Thue-Morse sequence. Preprint arXiv:1603.04434 (2017). [Google Scholar]
  24. A.M. Shur, The structure of the set of cube-free ℤ-words in a two-letter alphabet (Russian). Izv. Ross. Akad. Nauk Ser. Mat. 64 (2000) 201–224. English translation in Izv. Math. 64 (2000) 847–871. [CrossRef] [MathSciNet] [Google Scholar]
  25. N.J.A. Sloane et al., The on-line encyclopedia of integer sequences. Available at (2022). [Google Scholar]
  26. A. Thue, Über die gegenseitige Lage gleicher Teile gewisser Zeichenreihen. Norske vid. Selsk. Skr. Mat. Nat. Kl. 1 (1912) 1–67. Reprinted in Selected Mathematical Papers of Axel Thue, T. Nagell, editor, Universitetsforlaget, Oslo (1977) pp. 413–478. [Google Scholar]
  27. E. Zeckendorf, Représentation des nombres naturels par une somme de nombres de Fibonacci ou de nombres de Lucas. Bull. Soc. Roy. Liège 41 (1972) 179–182. [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.