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

preprint2015arXivOpen access

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 $n$ .

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

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