This material has been published in Graphs Combin. 21 (2005), 51-62, the only definitive repository of the content that has been certified and accepted after peer review. Copyright and all rights therein are retained by Springer-Verlag. This material may not be copied or reposted without explicit permission.

William Y. C. Chen, Arthur L. B. Yang and Christian Krattenthaler

The flagged Cauchy determinant

(12 pages)

Abstract. We consider a flagged form of the Cauchy determinant, for which we provide a combinatorial interpretation in terms of nonintersecting lattice paths. In combination with the standard determinant for the enumeration of nonintersecting lattice paths, we are able to give a new proof of the Cauchy identity for Schur functions. Moreover, by choosing different starting and end points for the lattice paths, we are led to a lattice path proof of an identity of Gessel which expresses a Cauchy-like sum of Schur functions in terms of the complete symmetric functions.

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