Grigory M Aug 21 at 17:42 feedback up vote 2 down vote Schur polynomials proof Observe that $D(a_1,\ldots,a_n)/D(1,\ldots,n)=s_\lambda(1,\ldots,1)$ (for $a_i=\lambda_i+i$). But by Giambelli (aka Jacobi-Trudi) formula $s_\lambda=\det h_{\lambda_i+j-1}$, so $s_\lambda(1,\ldots,1)=\det\binom{a_i}{j-1}$. Now by Lindstrom-Gessel-Viennot lemma last determinant counts non-intersecting lattice paths from the set $0,1,\ldots,n$ on Y-axis to the set $a_1,\ldots,a_n$ on