bibkey: li2025macmahon authors: Runqiao Li, Ali K. Uncu year: 2025 title: “A MacMahon Analysis View of Cylindric Partitions” doi: 10.48550/arXiv.2501.19272 url: https://arxiv.org/abs/2501.19272v1 claim: “Finite multiple-sum identities for cylindric partitions obtained by MacMahon’s Partition Analysis; proofs of finite Andrews–Gordon companion identities for k = 2, 3, 4 and Conjecture 1.3 for k ≥ 5.” strata_touched:

• D5/S3/Combinatorics/CylindricPartition/LiUncu license: citation-only triage: anchor

Li and Uncu, a MacMahon analysis view of cylindric partitions

The paper studies generating functions of cylindric partitions by MacMahon’s Partition Analysis and obtains finite polynomial identities of Rogers–Ramanujan and Andrews–Gordon type. Equation (1.5) compares a finite multiple sum of products of Gaussian binomials, with a doubled boundary shift 2α_{ij} and a primed convention for negative upper index, against an alternating sum of Gaussian binomials with a parity-dependent lower index. The paper proves the cases k = 2, 3, 4 and states the general case k ≥ 5, 1 ≤ i < k as Conjecture 1.3; the case i = k is the Foda–Quano identity.

The module D5/S3/Combinatorics/CylindricPartition/LiUncu proves Conjecture 1.3.

Verified locator

DOI: 10.48550/arXiv.2501.19272

URL: https://arxiv.org/abs/2501.19272v1

• Locator: Section 1, equation (1.5) and Conjecture 1.3.