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Ernst Snapper 《Journal of Combinatorial Theory, Series A》1979,26(1):65-81
Let G be a finite group. To each permutation representation (G, X) of G and class function χ of G we associate the χ-characteristic polynomialgχ(x) of (G, X) which is a polynomial in one variable with complex numbers as coefficients. The coefficients of gχ(x) are investigated in terms of the “exterior powers” of (G, X). If χ is the principal character 1G of G, the coefficients of gχ(x) are non-negative integers; and if furthermore G has odd order, the kth coefficient is the number of orbits of G acting on the subsets of X with k elements. Quadratic and linear relations among the exterior powers of (G, X) have been derived and it is shown how the polynomial gχ(x) can be computed from the cycle index of (G, X). 相似文献
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