  This paper proves an identity between flagged Schur polynomials, giving a
duality between row flags and column flags. This identity generalises both the
binomial determinant duality theorem due to Gessel and Viennot and the
symmetric function duality theorem due to Aitken. As corollaries we obtain the
lifts of the binomial determinant duality theorem to $q$-binomial coefficients
and to symmetric polynomials. Our method is a path counting argument on a novel
lattice generalising that used by Gessel and Viennot.
