Asymptotic distribution of odd-balanced unimodal sequences with rank congruent to a mod c

TL;DR

This paper derives an asymptotic estimate for odd balanced unimodal sequences with ranks congruent to a modulo c, revealing their relation to the overpartition function, contrasting with the partition function for strongly unimodal sequences.

Contribution

It provides the first asymptotic analysis for odd balanced unimodal sequences with specific rank congruences and uncovers their connection to the overpartition function.

Findings

Asymptotic estimate for odd balanced unimodal sequences with rank congruence

Relation between these sequences and the overpartition function

Contrast with strongly unimodal sequences related to the partition function

Abstract

We compute an asymptotic estimate for odd balanced unimodal sequences for ranks congruent to $a \pmod{c}$ for $c\neq 1$ odd. We find the interesting result that the odd balanced unimodal sequences are asymptotically related to the overpartition function. This is in contrast to strongly unimodal sequences which, are asymptotically related to the partition function.