Parity Indices and Two-Line Matrix Representation for Partitions

Authors

  • Irene Magalhães Craveiro UFGD-Universidade Federal da Grande Dourados
  • Adriana Wagner UFMS - Universidade Federal do Mato Grosso do Sul
  • Deborah Domingues IMECC-Unicamp

DOI:

https://doi.org/10.5540/tema.2015.016.03.0253

Keywords:

Partition, Parity index, Mock theta function

Abstract

In this work we present a solution for Andrews's Problem 5 [1], by establishing a bijection between the sets and defined in Fine's Theorem [8] and the sets of partitions indexed by their lower parity index [1]. We provide two combinatorial interpretations for [1], determining another solution for Problem 5. We also solve Andrews's Problem 6, conjectured in [1].

Author Biographies

Irene Magalhães Craveiro, UFGD-Universidade Federal da Grande Dourados

FACET - Faculdade de Ciências e Tecnologias - Curso de Matemática

Adriana Wagner, UFMS - Universidade Federal do Mato Grosso do Sul

Câmpus de Aquidauana - Curso de Matemática

Deborah Domingues, IMECC-Unicamp

aluna do Programa de Pós-Graduação do DMA.

References

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Brietzke, E.H.M.; Santos J.P.O.and Silva, R; Combinatorial interpretations as two-line array for the mock theta functions, Bulletin Brazilian Mathematical, 44 (2013) 233-253.

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R. Silva, J.C. Filho, and J.P.O. Santos, Proving Two Partition Identities , TEMA ,13 N.o 02 (2012), 133-142.

A.J. Yee, S.Kim, Göllnitz-Gordon Identities and Parity Questions in Partitions, European Journal of Combinatorics , 32, Issue 2, (2011) 288-293.

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

C.Wenchang, Two Problems of George Andrews on Generating Functions for partitions, Miskolc Mathematical Notes, Vol.13 (2012),No 2, pp. 293 -302.

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Published

2016-01-28

How to Cite

Craveiro, I. M., Wagner, A., & Domingues, D. (2016). Parity Indices and Two-Line Matrix Representation for Partitions. Trends in Computational and Applied Mathematics, 16(3), 253. https://doi.org/10.5540/tema.2015.016.03.0253

Issue

Vol. 16 No. 3 (2015)

Section

Original Article

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