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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

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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Additional Information

DOI: http://dx.doi.org/10.1090/S0025-5718-1984-0758206-7
PII: S 0025-5718(1984)0758206-7
Article copyright: © Copyright 1984 American Mathematical Society