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On Goulden-Jackson's Determinantal Formula for the Immanant
Matjaz Konvalinka
Department of Mathematics, Vanderbilt University, Nashville, TN 37240, USA
matjaz.konvalinka@vanderbilt.edu
Annals of Combinatorics 13 (4) pp.511-518 December, 2009
AMS Subject Classification: 05E10, 05E05
Abstract:
In 1992, Goulden and Jackson found a beautiful determinantal expression for the immanant of a matrix. This paper proves the same result combinatorially. We also present a b-extension of the theorem and a simple determinantal expression for the irreducible characters of the symmetric group.
Keywords: immanants, characters of the symmetric group, symmetric functions of eigenvalues, combinatorial proofs
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