Using Periodicity to Obtain Partition Congruences

TL;DR

This paper introduces a periodicity-based method to establish partition congruences, extending previous techniques to prove new and existing congruences for various restricted partition functions with limited calculations.

Contribution

It generalizes recent work by using periodicity to efficiently prove congruences for restricted partition and overpartition functions, broadening the scope of combinatorial congruence proofs.

Findings

Established new restricted plane partition congruences

Proved restricted plane overpartition congruences

Provided examples of restricted partition congruences

Abstract

In this paper, we generalize recent work of Mizuhara, Sellers, and Swisher that gives a method for establishing restricted plane partition congruences based on a bounded number of calculations. Using periodicity for partition functions, our extended technique could be a useful tool to prove congruences for certain types of combinatorial functions based on a bounded number of calculations. As applications of our result, we establish new and existing restricted plane partition congruences, restricted plane overpartition congruences and several examples of restricted partition congruences.