Generalizations of Cauchy's Determinant and Schur's Pfaffian

Mathematics – Combinatorics

Scientific paper

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26 pages

Scientific paper

We present several generalizations of Cauchy's determinant and Schur's
Pfaffian by considering matrices whose entries involve some generalized
Vandermonde determinants. Special cases of our formulae include previuos
formulae due to S.Okada and T. Sundquist. As an application, we give a relation
for the Littlewood--Richardson coefficients involving a rectangular partition.

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