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arXiv · 2610.40079

The bivariate generating function for cylindric partitions of rank three

Shane Chern·Trieu Nguyen·Chanh Tran·Tanay Wakhare
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Abstract

Using a rational analogue of an $\mathrm{A}_2^{(1)}$ Rogers--Ramanujan type identity discovered by Warnaar, we establish sum-like expressions for a bivariate generating function for cylindric partitions of rank three. These expressions provide the finishing touch towards conjectures of Warnaar and Kanade--Russell.

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Shane Chern, Trieu Nguyen, Chanh Tran, Tanay Wakhare. 2026-10-29. The bivariate generating function for cylindric partitions of rank three. https://arxiv.org/abs/2610.40079

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