Tight cylindric partitions
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866915454395613184 |
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| author | Kanade, Shashank Russell, Matthew C. |
| author_facet | Kanade, Shashank Russell, Matthew C. |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2508_15113 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Tight cylindric partitions Kanade, Shashank Russell, Matthew C. Combinatorics Quantum Algebra Representation Theory 05A15, 05A17, 11P84, 17B65, 17B69 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. |
| title | Tight cylindric partitions |
| topic | Combinatorics Quantum Algebra Representation Theory 05A15, 05A17, 11P84, 17B65, 17B69 |
| url | https://arxiv.org/abs/2508.15113 |