author = {K. Banerjee and N. A. Smoot},
title = {{The localization method applied to k-elongated plane partitions and divisibily by 5}},
language = {english},
abstract = {The enumeration $d_k(n)$ of k-elongated plane partition diamonds has emerged as a generalization of the classical integer partition function p(n). We have discovered an infinite congruence family for $d_5(n)$ modulo powers of 5. Classical methods cannot be used to prove this family of congruences. Indeed, the proof employs the recently developed localization method, and utilizes a striking internal algebraic structure which has not yet been seen in the proof of any congruence family. We believe that this discovery poses important implications on future work in partition congruences.},
number = {22-21},
year = {2022},
month = {August},
keywords = {Partition congruences, modular functions, plane partitions, partition analysis, Ramanujan’s theta functions, localization method, modular curve, Riemann surface},
length = {40},
license = {CC BY 4.0 International},
type = {RISC Report Series},
institution = {Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz},
address = {Altenberger Straße 69, 4040 Linz, Austria},
issn = {2791-4267 (online)}