# Asymptotic behavior of odd-even partitions

## TL;DR

This paper derives the asymptotic formula for odd-even partitions, revealing their long-term behavior, and explores related odd-even overpartitions, contributing to the understanding of these combinatorial structures in number theory.

## Contribution

It provides the first asymptotic analysis of odd-even partitions and investigates their overpartition counterparts, expanding knowledge of their combinatorial properties.

## Key findings

- Asymptotic formula for odd-even partitions derived
- Analysis of odd-even overpartitions included
- Enhanced understanding of combinatorial structures related to Ramanujan's identities

## Abstract

Andrews studied a function which appears in Ramanujan's identities. In Ramanujan's "Lost" Notebook, there are several formulas involving this function, but they are not as simple as the identities with other similar shape of functions. Nonetheless, Andrews found out that this function possesses combinatorial information, odd-even partition. In this paper, we provide the asymptotic formula for this combinatorial object. We also study its companion odd-even overpartitions.