A weighted generalization of Pólya's Enumeration Theorem is proved and applied to derive the determinant-trace identity as a signed cycle index of the symmetric group.
von Bell, P\' o lya's Enumeration Theorem and Its Applications, Master's Thesis, Univ
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An Extension of P\'{o}lya's Enumeration Theorem
A weighted generalization of Pólya's Enumeration Theorem is proved and applied to derive the determinant-trace identity as a signed cycle index of the symmetric group.