8 citations · 14 across the 14 of their papers we have counts for
15 papers
On the occurrence of congruence multiplicities between Ramanujan's theta functions
Shane Chern, Nicolas Allen Smoot, Dazhao Tang
Recently, the first and third authors initiated a study of arithmetical relationships between Ramanujan's theta functions and . In this work, we prove eight families…
Explaining Unforeseen Congruence Relationships Between PEND and POND Partitions via an Atkin--Lehner Involution
James A. Sellers, Nicolas Allen Smoot
For the past several years, numerous authors have studied POD and PED partitions from a variety of perspectives. These are integer partitions wherein the odd parts must be distinct…
On the Classification of Modular Congruence Families
Nicolas Allen Smoot
Congruence families, i.e., -adic convergence for well-defined arithmetic subsequences, is a commonplace phenomenon for the coefficients of modular forms. Such families superf…
Old Meets New: Connecting Two Infinite Families of Congruences Modulo Powers of 5 for Generalized Frobenius Partition Functions
Frank G. Garvan, James A. Sellers, Nicolas Allen Smoot
In 2012 Paule and Radu proved a difficult family of congruences modulo powers of 5 for Andrews' 2-colored generalized Frobenius partition function. The family is associated with th…
A Finite-Bound Partition Equinumerosity Result Generalizing a Solution of a Problem Posed by Andrews and Deutsch
Michael J. Schlosser, Nicolas Allen Smoot
We introduce a finite-bound extension of a partition equinumerosity result which was orignally proposed as a problem by Andrews and Deutsch in 2016, and given a generalized form in…
2-Elongated Plane Partitions and Powers of 7: The Localization Method Applied to a Genus 1 Congruence Family
Koustav Banerjee, Nicolas Allen Smoot
Over the last century, a large variety of infinite congruence families have been discovered and studied, exhibiting a great variety with respect to their difficulty. Major complica…
Divisibility Arising From Addition: The Application of Modular Functions to Infinite Partition Congruence Families
Nicolas Allen Smoot
The theory of partition congruences has been a fascinating and difficult subject for over a century now. In attempting to prove a given congruence family, multiple possible complic…
The Localization Method Applied to -Elongated Plane Partitions and Divisibility by 5
Koustav Banerjee, Nicolas Allen Smoot
The enumeration of -elongated plane partition diamonds has emerged as a generalization of the classical integer partition function . We have discovered an infinit…
On the Divisibility of 7-Elongated Plane Partition Diamonds by Powers of 8
James A. Sellers, Nicolas Allen Smoot
In 2021 da Silva, Hirschhorn, and Sellers studied a wide variety of congruences for the -elongated plane partition function by various primes. They also conjectured the…
A Congruence Family For 2-Elongated Plane Partitions: An Application of the Localization Method
Nicolas Allen Smoot
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…
On the Computation of Identities Relating Partition Numbers in Arithmetic Progressions with Eta Quotients: An Implementation of Radu's Algorithm
Nicolas Allen Smoot
In 2015 Cristian-Silviu Radu designed an algorithm to detect identities of a class studied by Ramanujan and Kolberg. This class includes the famous identities by Ramanujan which pr…
A Single-Variable Proof of the Omega SPT Congruence Family Over Powers of 5
Nicolas Allen Smoot
In 2018 Liuquan Wang and Yifan Yang proved the existence of an infinite family of congruences for the smallest parts function corresponding to the third order mock theta function $…
A Partition Function Connected with the Göllnitz--Gordon Identities
Nicolas Allen Smoot
We use the celebrated circle method of Hardy and Ramanujan to develop convergent formulae for counting a restricted class of partitions that arise from the Göllnitz--Gordon identit…
A Method of Verifying Partition Congruences by Symbolic Computation
Cristian-Silviu Radu, Nicolas Allen Smoot
Conjectures involving infinite families of restricted partition congruences can be difficult to verify for a number of individual cases, even with a computer. We demonstrate how th…
A Family of Congruences for Rogers--Ramanujan Subpartitions
Nicolas Allen Smoot
In 2015 Choi, Kim, and Lovejoy studied a weighted partition function, , which counted subpartitions with a structure related to the Rogers--Ramanujan identities. They conje…