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• W2613594615 abstract "Let f be a complex-valued function defined on a subgroup G of the symmetric group of a linearly ordered set with n elements. In this paper, the f-characteristics and f-descendants of G are defined. The f-characteristic of such group arises from the inner product space of all complex-valued functions on G and we note that the notion of characteristics generalizes Burnside’s Lemma. Loosely speaking, a characteristic is an average mass of a complex valued function on a permutation group. We give some properties of the characteristics and examples based on the factor groups, convolutions, sign of permutations and roots of unity. The study will then be restricted to functions on the symmetric, alternating and dihedral groups on {1,... , n} whose range lies in the set of nonnegative integers, which are called permutation statistics. Furthermore, we show that the inversion, descent, ascent and major index descendants of the dihedral group coincides." @default.
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• W2613594615 date "2012-01-01" @default.
• W2613594615 modified "2023-09-26" @default.
• W2613594615 title "The Characteristics and Descendants of Some Permutation Groups" @default.
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