On Goulden-Jackson’s Determinantal Formula for the Immanant

摘要

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 β-extension of the theorem and a simple determinantal expression for the irreducible characters of the symmetric group. AMS Subject Classification 05E10 - 05E05 Keywords immanants - characters of the symmetric group - symmetric functions of eigenvalues - combinatorial proofs