Enumeration by Weight
Now we are going to refine our methods in order to enumerate orbits with prescribed properties. For this purpose we introduce weight functions on X, i. e. mappings from X into commutative rings which are constant on the orbits of G on X. The Cauchy-Frobenius Lemma will be refined in order to count orbits with prescribed weight. We shall use it, for example, in order to enumerate graphs with prescribed numbers of vertices and edges. This leads us to certain generating functions, the cycle indicator polynomials.
KeywordsConjugacy Class Rooted Tree Formal Power Series Dihedral Group Symmetry Class
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