On the distribution of rank statistic for strongly concave compositions

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].