# Unimodal Sequence Generating Functions Arising from Partition Ranks

## TL;DR

This paper explores generating functions related to the rank of strongly unimodal sequences, providing combinatorial interpretations, identities involving mock modular forms, asymptotic analysis, and parity results, highlighting their connection to integer partition ranks.

## Contribution

It introduces new generating functions that model the rank of strongly unimodal sequences and establishes their combinatorial and modular properties, extending understanding of partition-related functions.

## Key findings

- Derived identities involving mock modular forms
- Established asymptotic behavior of the generating functions
- Proved a parity result for the functions

## Abstract

In this paper we study generating functions resembling the rank of strongly unimodal sequences. We give combinatorial interpretations, identities in terms of mock modular forms, asymptotics, and a parity result. Our functions imitate a relation between the rank of strongly unimodal sequences and the rank of integer partitions.