Proof of a conjecture of Andrews and El Bachraoui on the parity of two-color partitions

Koustav Banerjee; Kathrin Bringmann

paper

Proof of a conjecture of Andrews and El Bachraoui on the parity of two-color partitions

arXiv:2607.08369

Abstract

In this paper, we prove a conjecture of Andrews and El Bachraoui concerning the parity of certain two-color partitions. Precisely, we show that if the Fourier coefficient $t_{o} (n)$ of the corresponding $q$ -series is odd, then $8 n + 9$ is represented by the binary quadratic form $x^{2} + 2 y^{2}$ .