# Overpartitions Identities Involving Gaps and Weights

## TL;DR

This paper establishes a new identity linking overpartition functions with Rogers-Ramanujan-Gordon type overpartitions, focusing on weights and gaps, extending classical identities in partition theory.

## Contribution

It introduces a novel identity connecting overpartition functions and Rogers-Ramanujan-Gordon type overpartitions using weights and gaps, generalizing Alladi's weighted identity.

## Key findings

- Derived a new identity connecting overpartitions and Gordon-type overpartitions
- Extended classical identities in partition theory involving weights and gaps
- Provides a framework for further exploration of overpartition identities

## Abstract

In this paper, we find an identity which connects the overpartition function and the function of Rogers--Ramanujan--Gordon type overpartitions by considering the weights and gaps. This identity can be seen as an analogue of the weighted identity of Alladi.