Parity Indices and Two-Line Matrix Representation for Partitions

Irene Magalhães Craveiro, Adriana Wagner, Deborah Domingues

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].


Keywords


Partition; Parity index; Mock theta function

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References


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

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Trends in Computational and Applied Mathematics

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