= Determinantal form of a symmetric-group character
{title2=$[\lambda]=\det([\lambda_i-i+j])$}
Here $[a]$ is the trivial <character> of $S_a$, $[0]$ is the induction-product unit, $[a]=0$ for $a<0$, and multiplication is induction of external <tensor products>. The <Frobenius characteristic map> turns the expression into the <Jacobi–Trudi identity>. A sign-reversing involution on intersecting lattice-path systems leaves precisely the nonintersecting systems corresponding to <Semistandard Young tableaux>, proving the <determinant> identity.
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