The bivariate generating function for cylindric partitions of rank three

Source 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.