Proving Two Partition Identities

Authors

  • Robson da Silva Universidade Federal do ABC - UFABC
  • Jair Cunha Filho Universidade Federal de Itajubá
  • José Plínio Oliveira Santos Universidade Estadual de Campinas

DOI:

https://doi.org/10.5540/tema.2012.013.02.0133

Abstract

In this paper we give combinatorial proofs for two partition identities. The first one solves a recent open question formulated by G. E. Andrews.

Author Biographies

Robson da Silva, Universidade Federal do ABC - UFABC

Centro de Matemática, Computação e Cognição - CMCC

Jair Cunha Filho, Universidade Federal de Itajubá

Departamento de Matemática e Computação

José Plínio Oliveira Santos, Universidade Estadual de Campinas

Departamento de Matemática Aplicada

References

G.E. Andrews, “The Theory of Partitions”, Cambridge University Press, 1984.

G.E. Andrews, Parity in partition identities, The Ramanujan Journal, 23 (2010), 45–90.

J.C. Filho, “Variações do Diagrama de Ferrers, Partições Planas e Funções Geradoras”, Tese de Doutorado, IMECC, UNICAMP, Campinas, SP, 2006.

H. Göllnitz, "Einfache Partionen", Diplomarbeit W.S. 1960, Göttingen, 65 pp.

H. Göllnitz, Partitionen mit Differenzenbedingungen, J. Reine Angew. Math, 225(1967), 154-190.

B. Gordon, Some Ramanujan-like continued fractions, Abstracts of Short Communications, Int. Congr. of Math., 29-30, Stockholm, 1962.

B. Gordon, Some continued fractions of the Rogers-Ramanujan type, Duke Math. J., 31 (1965), 741-748.

A.J. Yee, Ramanujan’s partial theta series and parity in partitions, The Ramanujan Journal, 23 (2010), 215–225.

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Published

2012-06-01

How to Cite

da Silva, R., Filho, J. C., & Santos, J. P. O. (2012). Proving Two Partition Identities. Trends in Computational and Applied Mathematics, 13(2), 133–142. https://doi.org/10.5540/tema.2012.013.02.0133

Issue

Vol. 13 No. 2 (2012)

Section

Original Article

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