On the distribution of rank statistic for strongly concave compositions

TL;DR

This paper derives a uniform asymptotic formula for the rank statistic of strongly concave compositions, a specific type of integer partition with strict monotonic parts, building on prior work related to their generating functions.

Contribution

It provides the first uniform asymptotic formula for the rank statistic of strongly concave compositions, advancing understanding of their distribution.

Findings

Derived a uniform asymptotic formula for the rank statistic

Enhanced understanding of the distribution of strongly concave compositions

Builds on previous modularity results of the generating function

Abstract

A strongly concave composition of $n$ is an integer partition with strictly decreasing and increasing parts. In this paper we give a uniform asymptotic formula for the rank statistic of a strongly concave composition introduced by Andrews, Rhoades and Zwegers ['Modularity of the concave composition generating function', Algebra \& Number Theory 7 (2013), no. 9, 2103--2139].