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.

arXiv commentFinal version, 12 pages. To appear in Monatshefte für Mathematik