The Smith Normal Form of a Matrix Associated with Young's Lattice

Abstract

We prove a conjecture of Miller and Reiner on the Smith normal form of the operator $DU$ associated with a differential poset for the special case of Young's lattice. Equivalently, this operator can be described as $\frac{\partial }{\partial p_1}{p}_1$ acting on homogeneous symmetric functions of degree $n$.

10 pages