Parity Indices and Two-Line Matrix Representation for Partitions - Craveiro, Irene Magalhães; Wagner, Adriana; Domingues, Deborah (Trends in Computational and Applied Mathematics, 2016)
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].