Colored Partitions and the Fibonacci Sequence

J.P.O. Santos, M. Ivkovic

Abstract


We present interesting combinatorial interpretations for the Fibonacci numbers in terms of colored partitions obtained by using finite versions of two identities of the Rogers-Ramanujan type. New formula for the Fibonacci numbers is also given.

References


[1] P.Rr Adby and M.A.H. Dempster, “Introduction to Optimization Methods”, Chapman & Hall, London, 1974.

G.E. Andrews, “The Theory of Partitions”, Encyclopedia of Mathematics and Its Applications (Rota, Editor), Vol. 2, G.-C, Addison-Wesley, Reading, 1976. (Reissued: Cambridge University Press, London and New York, 1985).

G.E. Andrews, “q-Series: Their development and application in analysis, number theory, combinatorics, physics and computer algebra”, CBMS Regional Conf. Ser. in Math., no¯ 66, Amer. Math. Soc., Providence, R.I., 1986.

G.E. Andrews, Euler’s “Exemplum Memorabile Inductionis Fallacis and q-trinomio coefficients”, Dep. of Math. Penn State, Report # PM 65, May 1989.

G.E. Andrews, “Combinatorics and Ramanujan’s ‘lost’ notebook”, London Math. Soc. Lecture Note Series, No. 103, Cambridge Univ. Press, London, 1985, pp. 1-23.

G.E. Andrews, q-Trinomial Coefficients and Rogers-Ramanujan Type Identities, in Analytic Number Theory (B. Berndt ed.), Boston, 1990.

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

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

J.P.O. Santos, On the combinatorics of polynomial generalizations of Rogers- Ramanujan type identities, Discrete Mathematics, 254 No. 1-3 (2002), pp.497-511.

J.P.O. Santos and M. Ivkovi´c, Fibonacci Numbers and Partitions, Fibonacci Quarterly, 41 No. 3 (2003), 263-278.

J.P.O. Santos and P. Mondek, Extending Theorems of G¨ollnitz, A New Family of Partition Identities, The Ramanujan Journal, 3 (1999), 359-365.

J.P.O. Santos and A.V. Sills, q-Pell Sequences and Two Identities of V.S Lebesgue, Discrete Mathematics, 257, No. 1 (2002), 125-142.

L.J. Slater, Further identities of the Rogers-Ramanujan type, Proc. London Math. Soc. 54, No. 2 (1952), 147-167.

R. Tosi´c, Kombinatorika (in serbian). Univerzitet u Novom Sadu (1999), Novi Sad.




DOI: https://doi.org/10.5540/tema.2006.07.01.0119

Article Metrics

Metrics Loading ...

Metrics powered by PLOS ALM

Refbacks

  • There are currently no refbacks.


Trends in Computational and Applied Mathematics

A publication of the Brazilian Society of Applied and Computational Mathematics (SBMAC)

 

Indexed in:

                       

         

 

Desenvolvido por:

Logomarca da Lepidus Tecnologia