Cylindric-partition generating-function formulas for general k

Establish the conjectured generating-function formulas for CP_(2k−i,i−1)(n) and CP_(2k−i−1,i−1)(n) for every k≥4 and k≥i≥1, with the respective alternating bilateral q-binomial expressions specified in the conjecture.

Background

The paper verifies the analogous formulas for all pairs 4≥k≥i≥1 and then proposes continuation to k≥4. These expressions connect generating functions for two-row cylindric partitions with finite Andrews–Gordon- and Bressoud-type bilateral sums.

The conjecture is motivated by the observed persistence of the formulas in the explicitly computed small-profile cases. A general proof would provide a uniform description of these cylindric-partition generating functions.