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Mathematics of Computation

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An algorithm for the second immanant

Authors: Robert Grone and Russell Merris
Journal: Math. Comp. 43 (1984), 589-591
MSC: Primary 15A15; Secondary 05C50, 20C30
MathSciNet review: 758206
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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

$\displaystyle 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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Article copyright: © Copyright 1984 American Mathematical Society

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