Enumeration of diagonally colored Young diagrams

Abstract

In this note we give a new proof of a closed formula for the multivariable generating series of diagonally colored Young diagrams. This series also describes the Euler characteristics of certain Nakajima quiver varieties. Our proof is a direct combinatorial argument, based on Andrews’ work on generalized Frobenius partitions. We also obtain representations of these series in some particular cases as infinite products.