Fórmula Explícita e Interpretação Combinatória para os Números de Fibonacci

Authors

  • I.M. Craveiro
  • J.P.O. Santos

DOI:

https://doi.org/10.5540/tema.2004.05.02.0205

Abstract

Neste trabalho, damos uma nova interpretação combinatória para os números de Fibonacci em termos de partições restritas, fazendo uso do Símbolo de Frobenius. Também damos uma demonstração de uma conjectura para uma fórmula explícita de uma família de polinômios dada por Santos em [9].

References

[1] G.E. Andrews, q-Series: Their development and application in analysis, number theory, combinatorics, physics an computer algebra, “CBMS Regional Conference Series in Math.”, American Mathematical Society, Providence Rhode Island, Number 66, pp 87-93, 1986.

G.E. Andrews e R.J. Baxter, Lattice gas generalization of the hard hexagon model. III q-trinomio coeficientes, J. Stat. Phys., 47 (1987) 297-330.

G.E. Andrews. Generalized partitions, Mem. Amer.Math. Soc., 301 (1984) 1-44.

G.E. Andrews, “The theory of partitions”, Encyclopedia of Mathematics and its Applications, Vol.2, Cambridge University Press, London and New York, 1985.

G.E. Andrews, Combinatorics and Ramanujan’s “lost” notebook, “London Mathematical Society Lecture Notes Series”, Cambridge University Press, London, Number 103, pp 1-23, 1985.

G.E. Andrews, “Number Theory”, Dover Publications, New York, 1994.

P. Mondek, “Identidades de Slater: Novas identidades e interpretações combinat órias,” Tese de Doutorado, IMECC-UNICAMP, 1997.

J.P.O. Santos. On the combinatorics of polynomial generalizations of Rogers-Ramanujan type identities, Discrete Mathematics, 254 (2002) 497-511.

J.P.O. Santos, “Computer algebra and identities of the Rogers-Ramanujan type”, Ph.D. Thesis, Pennsylvania State University, 1991.

L.J. Slater, Further identities of the Rogers-Ramanujan type, Proc. London Math. Soc. (2), 54 (1952) 147-167.

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Published

2004-06-01

How to Cite

Craveiro, I., & Santos, J. (2004). Fórmula Explícita e Interpretação Combinatória para os Números de Fibonacci. Trends in Computational and Applied Mathematics, 5(2), 205–215. https://doi.org/10.5540/tema.2004.05.02.0205

Issue

Vol. 5 No. 2 (2004)

Section

Original Article

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