We give a bijective lattice path proof of the equality of the dual Jacobi-Trudy determinant formulas for Schur polynomials. Related ideas have appeared in [1, pp.304-306] and [2, p.24]. We remark that the same bijection works for the case of flagged skew Schur polynomials [2, 8] and that a determinant for $q$-counting restricted lattice paths  follows from the bijection.
"Bijective Lattice Path Proof of the Equality of the Dual Jacobi-Trudy Determinants." Tokyo J. Math. 14 (2) 341 - 343, December 1991. https://doi.org/10.3836/tjm/1270130377