# Congruences for Restricted Plane Overpartitions Modulo 4 and 8

## TL;DR

This paper establishes new congruence relations for plane overpartitions modulo 4 and 8, expanding understanding of their arithmetic properties through novel techniques.

## Contribution

It introduces new methods to prove congruences for restricted and unrestricted plane overpartitions modulo 4 and 8, building on prior generalizations.

## Key findings

- Proved congruences for plane overpartitions modulo 4 and 8
- Developed techniques applicable to restricted and unrestricted cases
- Extended previous results on overpartition congruences

## Abstract

In 2009, Corteel, Savelief and Vuleti\'c generalized the concept of overpartitions to a new object called plane overpartitions. In recent work, the author considered a restricted form of plane overpartitions called $k$-rowed plane overpartions and proved a method to obtain congruences for these and other types of combinatorial generating functions. In this paper, we prove several restricted and unrestricted plane overpartition congruences modulo $4$ and $8$ using other techniques.