English

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 d2(n)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 Z[X]\mathbb{Z}[X].

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>