Tight cylindric partitions

2025/08/20 by Kanade, Shashank, Russell, Matthew C. · 1 citation
#05A15 #05A17 #11P84 #17B65 #17B69 #Combinatorics (math.CO) #FOS: Mathematics #Quantum Algebra (math.QA) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2508.15113

Abstract

In this note, we initiate the study of generating functions for tight cylindric partitions. For general (i.e., r-rowed for r≥ 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.

Citations

• A Decomposition of Cylindric Partitions and Cylindric Partitions into Distinct Parts
• A proof of the second Rogers-Ramanujan identity via Kleshchev multipartitions
• Cylindric partitions and some new A₂ Rogers-Ramanujan identities
• The A₂ Rogers-Ramanujan identities revisited
• Periodic Schur process and cylindric partitions
• Branching functions of A_n-1⁽¹⁾ and Jantzen-Seitz problem for Ariki-Koike algebras

Cited by

• Affine Jacobi-Trudi formulas and q,t-Rogers-Ramanujan identities
• Grounded partitions of type A₁⁽¹⁾ at levels 1 and 2: bijections, affine crystal graphs, and partition identities

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