@**techreport**{RISC6382,author = {N. Smoot},

title = {{A Congruence Family For 2-Elongated Plane Partitions: An Application of the Localization Method}},

language = {english},

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 $mathbb{Z}[X]$.},

year = {2021},

month = {December},

institution = {Research Institute for Symbolic Computation, JKU Linz},

keywords = {Partition congruences, modular functions, plane partitions, partition analysis, localization method, modular curve, Riemann surface},

sponsor = {Austrian Science Fund (FWF): Einzelprojekte P 33933.},

length = {28}

}