A Congruence Family For 2-Elongated Plane Partitions: An Application of the Localization Method

Abstract

George Andrews and Peter Paule have recently conjectured an infinite family of congruences modulo powers of 3 for the 2-elongated plane partition function $d_2(n)$. This congruence family appears difficult to prove by classical methods. We prove a refined form of this conjecture by expressing the associated generating functions as elements of a ring of modular functions isomorphic to a localization of $\mathbb{Z}[X]$.

31 pages, 2 figures, 3 tables. References a Mathematica supplement which can be found online at <https://www.risc.jku.at/people/nsmoot/2eplanepartsupplement.nb>

References in corpus (1)

• A Single-Variable Proof of the Omega SPT Congruence Family Over Powers of 5

Cited by in corpus (2)

• Old Meets New: Connecting Two Infinite Families of Congruences Modulo Powers of 5 for Generalized Frobenius Partition Functions
• 2-Elongated Plane Partitions and Powers of 7: The Localization Method Applied to a Genus 1 Congruence Family