In the course of our investigation of counting problems we have encountered many functions c = c(k) depending on an integral parameter k = 0, 1, 2,.... Most of the time the parameter had something to do with the type classification of the underlying incidence algebra. Our goal is now to find the solution c(0), c(1), c(2),...in a closed form instead of having to evaluate each term c(k) individually. To accomplish this we regard c(k) = c k as coefficient of a formal power series and develop methods to compute this series, called the generating function for the coefficients c k .
KeywordsBoolean Function Rooted Tree Permutation Group Label Graph Counting Problem
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