This is the Second Edition of the highly successful introduction to the use of generating functions and series in combinatorial mathematics. This new edition includes several new areas of application, including the cycle index of the symmetric group, permutations and square roots, counting polyominoes, and exact covering sequences. An appendix on using the computer algebra programs MAPLE(r) and Mathematica (r) to generate functions is also included. The book provides a clear, unified introduction to the basic enumerative applications of generating functions, and includes exercises and solutions, many new, at the end of each chapter.
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Cards Decks and Hands The Exponential Formula
Applications of generating functions
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analytic answer asymptotic average number Bell numbers binomial coefficient bipartite graph cards chapter choose coefficient of xn combinatorial computation connected graphs converges counting cyclotomic polynomials deck defined disk divisors equation exact covering exactly example explicit formula exponential family exponential formula exponential generating function Fibonacci Fibonacci numbers fixed points formal power series given hand enumerator hands of weight Hence identity in}o left side legal string Lemma letters multiply N(D S nonnegative integers number of cycles number of hands number of objects number of partitions number of permutations obtain opsgf ordinary power series pairs parentheses polynomial polyominoes positive integers prefab problem proof prove recurrence formula recurrence relation result rooted trees roots of unity series generating function Show sieve method singularities Snake Oil Snake Oil method solve Stirling numbers subset summation Suppose theorem unimodal values vertex vertices xn and sum zeros