Partition Congruences by the Localization Method

Project Lead

Project Duration

01/03/2021 - 28/02/2023

Publications

2021

[Smoot]

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

N. Smoot

Research Institute for Symbolic Computation, JKU Linz. Technical report, December 2021. [pdf]
[bib]
@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}
}

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