A Congruence Family For 2-Elongated Plane Partitions: An Application of the Localization Method
Number Theory
2022-08-26 v4
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 . 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 .
Keywords
Cite
@article{arxiv.2111.07131,
title = {A Congruence Family For 2-Elongated Plane Partitions: An Application of the Localization Method},
author = {Nicolas Allen Smoot},
journal= {arXiv preprint arXiv:2111.07131},
year = {2022}
}
Comments
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>