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

Nicolas Smoot

doi:10.1016/j.jnt.2022.07.014

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

Nicolas Smoot

Research Institute for Symbolic Computation

Research output: Contribution to journal › Article › peer-review

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 $mathbb{Z}[X]$.

Original language	English
Pages (from-to)	112-153
Number of pages	42
Journal	Journal of Number Theory
Volume	242
DOIs	https://doi.org/10.1016/j.jnt.2022.07.014
Publication status	Published - Jan 2023

Fields of science

101 Mathematics
101001 Algebra
101005 Computer algebra
101009 Geometry
101012 Combinatorics
101013 Mathematical logic
101020 Technical mathematics

JKU Focus areas

Digital Transformation

Access to Document

10.1016/j.jnt.2022.07.014

Cite this

@article{eeaa140482144d00adc0850b54313862,

title = "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 \$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]\$.",

author = "Nicolas Smoot",

year = "2023",

month = jan,

doi = "10.1016/j.jnt.2022.07.014",

language = "English",

volume = "242",

pages = "112--153",

journal = "Journal of Number Theory",

issn = "1096-1658",

publisher = "Elsevier",

}

TY - JOUR

T1 - A Congruence Family For 2-Elongated Plane Partitions: An Application of the Localization Method

AU - Smoot, Nicolas

PY - 2023/1

Y1 - 2023/1

N2 - 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 $mathbb{Z}[X]$.

AB - 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 $mathbb{Z}[X]$.

UR - https://www.scopus.com/pages/publications/85144041060

U2 - 10.1016/j.jnt.2022.07.014

DO - 10.1016/j.jnt.2022.07.014

M3 - Article

SN - 1096-1658

VL - 242

SP - 112

EP - 153

JO - Journal of Number Theory

JF - Journal of Number Theory

ER -

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

Abstract

Fields of science

JKU Focus areas

Access to Document

Other files and links

Cite this