An algorithm for the second immanant

Abstract

Let χ \chi be an irreducible character of the symmetric group S n {S_n} . For A = ( a i j ) A = ({a_{ij}}) an n-by-n matrix, define the immanant of A corresponding to χ \chi by \[ d ( A ) = ∑ σ ∈ S n χ ( σ ) ∏ t = 1 n a t σ ( t ) . d(A) = \sum \limits _{\sigma \in {S_n}} {\chi (\sigma )\prod \limits _{t = 1}^n {{a_{t\sigma (t)}}.} } \] The article contains an algorithm for computing d ( A ) d(A) when χ \chi corresponds to the partition (2, 1 n − 2 {1^{n - 2}} ).