Linking Congruences for PED and POD partitions

TL;DR

This paper explores the relationships between congruences in PED and POD partitions and overpartition families, revealing natural links and extending understanding of partition congruences.

Contribution

It introduces new connections between congruences for PED and POD partitions and overpartitions, expanding the framework of partition congruence relationships.

Findings

PED and POD partitions are linked to overpartition congruences

New congruence families for PED and POD partitions identified

Connections extend the theory of partition congruences

Abstract

Recent work of Garvan, Sellers, Smoot, and others has made connections between infinite families of congruences for various partition functions. Here, we apply this approach to families of congruences for PED and POD partitions and find that they are naturally linked to congruence families for overpartitions into odd parts and overpartitions.