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math.NT2022
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…
math.NT2022
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…
math.NT2022
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…