ABSTRACT
In this work we present a solution for Andrews's Problem 511 G.E. Andrews. Parity in partition identities. Ramanujan Journal, 23 (2010), 45-90. by establishing a bijection between the sets and defined in Fine's Theorem88 I. Pak. On Fine's partition theorems, Dyson, Andrews and missed opportunities. Mathematical Intel- ligencer, 25(1) (2003), p. 10. and the sets of partitions indexed by their lower parity index11 G.E. Andrews. Parity in partition identities. Ramanujan Journal, 23 (2010), 45-90.. We also solve Andrews's Problem 6, conjectured in11 G.E. Andrews. Parity in partition identities. Ramanujan Journal, 23 (2010), 45-90..
Keywords:
partition; parity index; mock theta function