Refined parity biases in integer partitions

Abstract

Recently, the authors and Jeremy Lovejoy proved that there is a parity bias in integer partitions, namely po(n)>pe(n) for all positive integers n≠2, where po(n) (resp. pe(n)) is the number of partitions of n with more odd (resp. even) parts than even (resp. odd) parts. In this paper, we give two refinements of the parity bias in integer partitions. © 2022 Elsevier B.V.