An algorithm for the second immanant

Grone, Robert; Merris, Russell

doi:10.1090/S0025-5718-1984-0758206-7

An algorithm for the second immanant
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by Robert Grone and Russell Merris PDF

Math. Comp. 43 (1984), 589-591 Request permission

Abstract:

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

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