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 d2(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 Z[X].
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