Tight cylindric partitions

In this note, we initiate the study of generating functions for tight cylindric partitions. For general (i.e., r r -rowed for r ≥ 2 r\geq 2 ) tight cylindric partitions, we provide analogues of the Corteel–Welsh functional equations. We prove closed forms for the bivariate generating functions for two-rowed tight cylindric partitions. We also show that these partitions are in bijection with a class of partitions studied by Dousse, Hardiman, and Konan [Proc. Amer. Math. Soc. 153 (2025), pp. 1363–1382].