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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
DOI: https://doi.org/10.1090/S0025-5718-1984-0758206-7
MathSciNet review: 758206
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Abstract | References | Similar Articles | Additional Information

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}}$).

References [Enhancements On Off] (What's this?)

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  • [4] R. Merris, "Representations of $ GL(n,R)$ and generalized matrix functions of class MPW," Linear and Multilinear Algebra, v. 11, 1982, pp. 133-141. MR 650727 (83e:15009)
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Additional Information

DOI: https://doi.org/10.1090/S0025-5718-1984-0758206-7
Article copyright: © Copyright 1984 American Mathematical Society

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