Generalization of the Fibonacci multiplication

Ali Messaoudi

Mathematica Slovaca (2000)

  • Volume: 50, Issue: 2, page 135-148
  • ISSN: 0232-0525

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Messaoudi, Ali. "Généralisation de la multiplication de Fibonacci." Mathematica Slovaca 50.2 (2000): 135-148. <http://eudml.org/doc/34511>.

@article{Messaoudi2000,
author = {Messaoudi, Ali},
journal = {Mathematica Slovaca},
keywords = {multiplication of Fibonacci; recurrent sequences},
language = {fre},
number = {2},
pages = {135-148},
publisher = {Mathematical Institute of the Slovak Academy of Sciences},
title = {Généralisation de la multiplication de Fibonacci},
url = {http://eudml.org/doc/34511},
volume = {50},
year = {2000},
}

TY - JOUR
AU - Messaoudi, Ali
TI - Généralisation de la multiplication de Fibonacci
JO - Mathematica Slovaca
PY - 2000
PB - Mathematical Institute of the Slovak Academy of Sciences
VL - 50
IS - 2
SP - 135
EP - 148
LA - fre
KW - multiplication of Fibonacci; recurrent sequences
UR - http://eudml.org/doc/34511
ER -

References

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  1. ARNOUX P., Un exemple de semi-conjugaison entre un échange d'intervalles et une rotation sur le tore, Bull. Soc. Math. France 116 (1988), 489-500. (1988) MR1005392
  2. ARNOUX P., Some remarks about Fibonacci multiplication, Appl. Math. Lett. 2 (1989), 319-320. (1989) Zbl0711.11008MR1025844
  3. BRAUER A., On algebraic equations with all but one root in the interior of the unit circle, Math. Nachr. 4 (1951), 250-257. (1951) Zbl0042.01501MR0041975
  4. CHEKHOVA N.-HUBERT P.-MESSAOUDI A., Propriétés combinatoires, ergodiques et arithmétiques de la substitution de Fibonacci, Preprint de ľlnstitut de mathématiques de Luminу. 
  5. DUMONT J. M., Formules sommatoires et systèmes de numération liés aux substitutions, Sém. Théor. Nombres Bordeaux (2), Univ. Bordeaux I, Talence, 1987-88. (1987) 
  6. DUMONT J. M.-THOMAS A., Systèmes de numération et fonctions fractales relatifs aux substitutions, Theor. Comput. Sci. 65 (1989), 153-169. (1989) Zbl0679.10010MR1020484
  7. DUMONT J. M.-THOMAS A., Digital sum problems and substitution on a finite alphabet, Preprint. MR1133561
  8. FRAENKEL A. S., Systems of numeration, Amer. Math. Monthlу 92 (1985), 105-114. (1985) Zbl0568.10005MR0777556
  9. FRAENKEL A. S.-PORTA H. A.-STOLARSKY K. B., Some arithmetical semi groups, In: Proc. International Conf. on Analуtic Number Theorу (B. Berndt et al., eds.), Birkauser, Boston, 1990, pp. 255-264. (1990) MR1084184
  10. FROUGNY C., Representation of numbers and finite automata, Math. Systems Theory 25 (1992), 37-60. (1992) MR1139094
  11. FROUGNY C., How to write integers in non-integer base, In: Latin 92, Sao Paulo, Vol. 583. Lecture Notes in Comput. Sci., Springer, New York, 1992, pp. 154-164. (1992) MR1253354
  12. FROUGNY C., Fibonacci representations and Finite automata, IEEE Trans. Inform. Theory 37 (1991), 393-399. (1991) Zbl0716.68067MR1093759
  13. FROUGNY C.- SOLOMYAK B., Finite Beta-expansions, Ergodic Theory Dynam. Systems 12 (1992), 713-723. (1992) MR1200339
  14. GRABNER J.- PETHO A.- TICHY R. F.- WOEGINGER J., Associativity of Recurrence Multiplication, Appl. Math. Lett. 7 (1994), 85-90. (1994) MR1350398
  15. GRABNER P. J.- TICHY R. F., Contributions to digit expansions with respect to linear recurrences, J. Number Theory 36 (1990), 160-169. (1990) MR1072462
  16. GRABNER P. J.- TICHY R. F., α expansions, linear recurrences and the sum of digits functions, Manuscripta Math. 70 (1991), 311-324. (1991) MR1089067
  17. HEDLUND G. A.- MORSE M., Symbolic dynamics, Amer. J. Math. 60 (1938), 815-866. (1938) MR1507944
  18. HEDLUND G. A.- MORSE M., Symbolic dynamics, part II: Sturmian trajectories, Amer. J. Math. 62 (1940), 1-42. (1940) MR0000745
  19. ITO S.- KIMURA M., On the Rauzy fractal, Japan J. Indust. Appl. Math. 8 (1991), 461-486. (1991) MR1137652
  20. KNUTH D. E., Fibonacci multiplication, Appl. Math. Lett. 1, 57-60. Zbl0633.10011MR0947168
  21. MESSAOUDI A., Autour du fractal de Rauzy, These d'Universite, Aix-Marseille II, 96. 
  22. MESSAOUDI A., Propriétés arithmetiques et dynamiques du fractal de Rauzy, J. Théor. Nombres Bordeaux 10 (1998), 135-161. (1998) Zbl0918.11048MR1827290
  23. MESSAOUDI A., Frontiére du fractal de Rauzy et systéme de numération complexe, Acta Arith. (To appear) [Prepublication de l'Institut de mathematiques de Luminy, numéro 97-25]. Zbl0968.28005MR1793161
  24. PETHO A.- TICHY R. F., On digit expansions with respect to linear recurrences, J. Number Theory 33 (1989), 243-256. (1989) MR1034204
  25. QUEFFELEC M., Substitution Dynamical Systems-Spectral Analysis, Lecture Notes in Mathematics 1294, Springer-Verlag, Berlin, 1987. (1987) Zbl0642.28013MR0924156
  26. RAUZY G., Nombres algébriques et substitutions, Bull. Soc. Math. France 110 (1982), 147-178. (1982) Zbl0522.10032MR0667748
  27. SIRVENT V., Properties of Geometrical Realisations of Substitutions Associated to a Family of Pisot Numbers, Thése, Mars 93. 
  28. SIRVENT V., Relationships between the dynamical systems associated to the Rauzy substitutions, Theoret. Comput. Sci. 164 (1996), 41-57. (1996) Zbl0873.58030MR1411197
  29. SIRVENT V., On some dynamical subsets of the Rauzy fractal, Theoret. Comput. Sci. 180 (1997), 363-370. (1997) Zbl0896.28002MR1453876
  30. ZECKENDORF E., Représentation des nombres naturels par une somme de nombres de Fibonacci ou de nombres de Lucas, Bull. Soc. Roy. Sci. Liége 41 (1972), 179-182. (1972) Zbl0252.10011MR0308032

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