# Orthogonal polynomials and Smith normal form

@article{Miller2017OrthogonalPA, title={Orthogonal polynomials and Smith normal form}, author={Alexander R. Miller and Dennis Stanton}, journal={Monatshefte f{\"u}r Mathematik}, year={2017}, volume={187}, pages={125-145} }

Smith normal form evaluations found by Bessenrodt and Stanley for some Hankel matrices of q-Catalan numbers are proven in two ways. One argument generalizes the Bessenrodt–Stanley results for the Smith normal form of a certain multivariate matrix that refines one studied by Berlekamp, Carlitz, Roselle, and Scoville. The second argument, which uses orthogonal polynomials, generalizes to a number of other Hankel matrices, Toeplitz matrices, and Gram matrices. It gives new results for q-Catalan…

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