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arXiv · 2508.15113

Tight cylindric partitions

Shashank Kanade·Matthew C. Russell
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Abstract

In this note, we initiate the study of generating functions for tight cylindric partitions. For general (i.e., $r$-rowed for $r\geq 2$) tight cylindric partitions, we provide analogs of the Corteel--Welsh functional equations. We prove closed forms for the bivariate generating functions for 2-rowed tight cylindric partitions. We also show that these partitions are in bijection with a class of partitions studied by Dousse, Hardiman, and Konan.

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Shashank Kanade, Matthew C. Russell. 2025-08-20. Tight cylindric partitions. https://arxiv.org/abs/2508.15113

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