** 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.
** AMS Classification: **
05E05, 05A15
** Keywords: **
divided difference, Cauchy identity, flagged Cauchy determinant, multi-Schur
function, nonintersecting lattice paths
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