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

Koustav Banerjee; Kathrin Bringmann

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arXiv · 2607.08369

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

Koustav Banerjee·Kathrin Bringmann

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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 $8n+9$ is represented by the binary quadratic form $x^2+2y^2$.

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Koustav Banerjee, Kathrin Bringmann. 2026-07-09. Proof of a conjecture of Andrews and El Bachraoui on the parity of two-color partitions. https://arxiv.org/abs/2607.08369

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