Biases in non-unitary partitions

Abstract

Recently, the concept of parity bias in integer partitions has been studied by several authors. We continue this study here, but for non-unitary partitions (namely, partitions with parts greater than 1). We prove analogous results for these restricted partitions to those that have been obtained by Kim et al. (Eur J Combin 89:103159, 2020), Kim and Kim (Bull Aust Math Soc 104(2): 177–186, 2021). We also look at inequalities between two classes of partitions studied by Andrews (Ann Comb 23(2), 241–248, 2019), where the parts are separated by parity (either all odd parts are smaller than all even parts or vice versa). © The Author(s) 2026.