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Introductory Ideas and Examples
Cards Decks and Hands The Exponential Formula
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an}o analytic answer average number Bell numbers binomial coefficient binomial type bipartite graph cards choose closed form coefficient of xn combinatorial computation connected graphs counting defined disk divisors exactly example explicit formula exponential family exponential formula exponential generating function Fibonacci Fibonacci numbers formal power series free variable function f(z given hand enumerator hands of weight Hence identity label sets labeled graphs left side legal string Lemma Let f(z letters log concave N(D S nonnegative integers number of hands number of objects number of partitions number of permutations opsgf ordinary power series pair parentheses partial fraction poles polynomial positive integers prefab problem proof prove radius of convergence rational function recurrence relation relabeling result rooted trees series generating function sieve method singularities Snake Oil method solve Stirling numbers subset summation Suppose theorem unimodal values vertex vertices xn and sum xn/n zeros