Title:
|
Généralisation de la multiplication de Fibonacci (French) |
Title:
|
Generalization of the Fibonacci multiplication (English) |
Author:
|
Messaoudi, Ali |
Language:
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French |
Journal:
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Mathematica Slovaca |
ISSN:
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0139-9918 |
Volume:
|
50 |
Issue:
|
2 |
Year:
|
2000 |
Pages:
|
135-148 |
. |
Category:
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math |
. |
MSC:
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11B39 |
idZBL:
|
Zbl 0984.11009 |
idMR:
|
MR1763116 |
. |
Date available:
|
2009-09-25T11:43:29Z |
Last updated:
|
2012-08-01 |
Stable URL:
|
http://hdl.handle.net/10338.dmlcz/136773 |
. |
Reference:
|
[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. MR 1005392 |
Reference:
|
[2] ARNOUX P.: Some remarks about Fibonacci multiplication.Appl. Math. Lett. 2 (1989), 319-320. Zbl 0711.11008, MR 1025844 |
Reference:
|
[3] BRAUER A.: On algebraic equations with all but one root in the interior of the unit circle.Math. Nachr. 4 (1951), 250-257. Zbl 0042.01501, MR 0041975 |
Reference:
|
[4] CHEKHOVA N.-HUBERT P.-MESSAOUDI A.: Propriétés combinatoires, ergodiques et arithmétiques de la substitution de Fibonacci.Preprint de ľlnstitut de mathématiques de Luminу. |
Reference:
|
[5] DUMONT J. M.: Formules sommatoires et systèmes de numération liés aux substitutions.Sém. Théor. Nombres Bordeaux (2), Univ. Bordeaux I, Talence, 1987-88. |
Reference:
|
[6] DUMONT J. M.-THOMAS A.: Systèmes de numération et fonctions fractales relatifs aux substitutions.Theor. Comput. Sci. 65 (1989), 153-169. Zbl 0679.10010, MR 1020484 |
Reference:
|
[7] DUMONT J. M.-THOMAS A.: Digital sum problems and substitution on a finite alphabet.Preprint. MR 1133561 |
Reference:
|
[8] FRAENKEL A. S.: Systems of numeration.Amer. Math. Monthlу 92 (1985), 105-114. Zbl 0568.10005, MR 0777556 |
Reference:
|
[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. MR 1084184 |
Reference:
|
[10] FROUGNY C.: Representation of numbers and finite automata.Math. Systems Theory 25 (1992), 37-60. MR 1139094 |
Reference:
|
[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. MR 1253354 |
Reference:
|
[12] FROUGNY C.: Fibonacci representations and Finite automata.IEEE Trans. Inform. Theory 37 (1991), 393-399. Zbl 0716.68067, MR 1093759 |
Reference:
|
[13] FROUGNY C.- SOLOMYAK B.: Finite Beta-expansions.Ergodic Theory Dynam. Systems 12 (1992), 713-723. MR 1200339 |
Reference:
|
[14] GRABNER J.- PETHO A.- TICHY R. F.- WOEGINGER J.: Associativity of Recurrence Multiplication.Appl. Math. Lett. 7 (1994), 85-90. MR 1350398 |
Reference:
|
[15] GRABNER P. J.- TICHY R. F.: Contributions to digit expansions with respect to linear recurrences.J. Number Theory 36 (1990), 160-169. MR 1072462 |
Reference:
|
[16] GRABNER P. J.- TICHY R. F.: α expansions, linear recurrences and the sum of digits functions.Manuscripta Math. 70 (1991), 311-324. MR 1089067 |
Reference:
|
[17] HEDLUND G. A.- MORSE M.: Symbolic dynamics.Amer. J. Math. 60 (1938), 815-866. MR 1507944 |
Reference:
|
[18] HEDLUND G. A.- MORSE M.: Symbolic dynamics, part II: Sturmian trajectories.Amer. J. Math. 62 (1940), 1-42. MR 0000745 |
Reference:
|
[19] ITO S.- KIMURA M.: On the Rauzy fractal.Japan J. Indust. Appl. Math. 8 (1991), 461-486. MR 1137652 |
Reference:
|
[20] KNUTH D. E.: Fibonacci multiplication.Appl. Math. Lett. 1, 57-60. Zbl 0633.10011, MR 0947168 |
Reference:
|
[21] MESSAOUDI A.: Autour du fractal de Rauzy.These d'Universite, Aix-Marseille II, 96. |
Reference:
|
[22] MESSAOUDI A.: Propriétés arithmetiques et dynamiques du fractal de Rauzy.J. Théor. Nombres Bordeaux 10 (1998), 135-161. Zbl 0918.11048, MR 1827290 |
Reference:
|
[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]. Zbl 0968.28005, MR 1793161 |
Reference:
|
[24] PETHO A.- TICHY R. F.: On digit expansions with respect to linear recurrences.J. Number Theory 33 (1989), 243-256. MR 1034204 |
Reference:
|
[25] QUEFFELEC M.: Substitution Dynamical Systems-Spectral Analysis.Lecture Notes in Mathematics 1294, Springer-Verlag, Berlin, 1987. Zbl 0642.28013, MR 0924156 |
Reference:
|
[26] RAUZY G.: Nombres algébriques et substitutions.Bull. Soc. Math. France 110 (1982), 147-178. Zbl 0522.10032, MR 0667748 |
Reference:
|
[27] SIRVENT V.: Properties of Geometrical Realisations of Substitutions Associated to a Family of Pisot Numbers.Thése, Mars 93. |
Reference:
|
[28] SIRVENT V.: Relationships between the dynamical systems associated to the Rauzy substitutions.Theoret. Comput. Sci. 164 (1996), 41-57. Zbl 0873.58030, MR 1411197 |
Reference:
|
[29] SIRVENT V.: On some dynamical subsets of the Rauzy fractal.Theoret. Comput. Sci. 180 (1997), 363-370. Zbl 0896.28002, MR 1453876 |
Reference:
|
[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. Zbl 0252.10011, MR 0308032 |
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