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PreprintarXiv licencearXiv

The bivariate generating function for cylindric partitions of rank three

  • Shane Chern
  • Trieu Nguyen
  • Chanh Tran
  • Tanay Wakhare
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Abstract

Using a rational analogue of an A2(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.

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Cite

BibTeXRIS
BibTeX
@misc{chern2026bivariate,
  title = {{The bivariate generating function for cylindric partitions of rank three}},
  author = {Shane Chern and Trieu Nguyen and Chanh Tran and Tanay Wakhare},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.40079},
  eprint = {2610.40079},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.40079},
}
RIS
TY  - UNPB
TI  - The bivariate generating function for cylindric partitions of rank three
AU  - Shane Chern
AU  - Trieu Nguyen
AU  - Chanh Tran
AU  - Tanay Wakhare
PY  - 2026
DA  - 2026/10/29
PB  - arXiv
DO  - 10.48550/arxiv.2610.40079
UR  - https://arxiv.org/abs/2610.40079
AB  - Using a rational analogue of an 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.
ER  -