On conjectures of Chern concerning parity bias in partitions

TL;DR

This paper proves conjectures by Chern that establish the nonnegativity of a q-series connected to parity bias in integer partitions, advancing understanding in partition theory.

Contribution

It provides a proof for Chern's conjectures on the nonnegativity of a specific q-series related to parity bias in partitions.

Findings

Confirmed nonnegativity of the q-series in question

Validated Chern's conjectures on parity bias

Contributed to the theory of integer partitions

Abstract

We prove recent conjectures of Chern concerning nonnegativity of a certain q-series related to parity bias in integer partitions.