Refined parity biases in integer partitions

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 not equal 2, where p(o)(n) (resp. p(e)(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. (c) 2022 Elsevier B.V. All rights reserved.