The Flagged Cauchy Determinant
William Y. C. Chen, C. Krattenthaler and Arthur L. B. Yang
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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. Keywords: Divided difference, Cauchy theorem, flagged Cauchy determinant, multi-Schur function, lattice paths. Download: ps |