# The Bressoud-G\"ollnitz-Gordon Theorem for Overpartitions of even moduli

## TL;DR

This paper establishes an overpartition analogue of Bressoud's generalization of the G"ollnitz-Gordon theorem for even moduli, demonstrating a combinatorial equality between two classes of overpartitions under certain conditions.

## Contribution

It introduces a new overpartition analogue of a classical theorem, extending the combinatorial framework to overpartitions for even moduli.

## Key findings

- Proves the equality O_{k,i}(n)=P_{k,i}(n) for specified parameters.
- Extends classical partition theorems to overpartition settings.
- Provides combinatorial identities for overpartitions with difference and congruence conditions.

## Abstract

We give an overpartition analogue of Bressoud's combinatorial generalization of the G\"ollnitz-Gordon theorem for even moduli in general case. Let $\widetilde{O}_{k,i}(n)$ be the number of overpartitions of $n$ whose parts satisfy certain difference condition and $\widetilde{P}_{k,i}(n)$ be the number of overpartitions of $n$ whose non-overlined parts satisfy certain congruence condition. We show that $\widetilde{O}_{k,i}(n)=\widetilde{P}_{k,i}(n)$ for $1\leq i<k$.