An inequality between finite analogues of rank and Crank moments

Abstract

The inequality between rank and crank moments was conjectured and later proved by Garvan himself in 2011. Recently, Dixit and the authors introduced finite ana- logues of rank and crank moments for vector partitions while deriving a finite analogue of Andrews’ famous identity for smallest parts function. In the same paper, they also con- jectured an inequality between finite analogues of rank and crank moments, analogous to Garvan’s conjecture. In the present paper, we give a proof of this conjecture