Asymptotics of parity biases for partitions into distinct parts via Nahm sums

Abstract

AbstractFor a random partition, one of the most basic questions is: what can one expect about the parts that arise? For example, what is the distribution of the parts of random partitions modulo ? As most partitions contain a 1, and indeed many 1s arise as parts of a random partition, it is natural to expect a skew toward . This is indeed the case. For instance, Kim, Kim, and Lovejoy recently established “parity biases” showing how often one expects partitions to have more odd than even parts. Here, we generalize their work to give asymptotics for biases for partitions into distinct parts. The proofs rely on the Circle Method and give independently useful techniques for analyzing the asymptotics of Nahm‐type ‐hypergeometric series.