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62 reviewsState of the art, Handbook of Enumerative Combinatorics brings together the work of today’s most prominent researchers. The contributors survey the methods of combinatorial enumeration along with the most frequent applications of these methods.
Edited by Miklós Bóna, University of Florida where he is a member of the Academy of Distinguished Teaching Scholars. He received his Ph.D. in mathematics at MIT in 1997. Miklós is the author of four books and more than 65 research articles, including the award-winning Combinatorics of Permutations. Miklós Bóna is an editor-in-chief for the Electronic Journal of Combinatorics and Series Editor of the Discrete Mathematics and Its Applications Series.
The first two chapters provide a comprehensive overview of the most frequently used methods in combinatorial enumeration, including algebraic, geometric, and analytic methods. These chapters survey generating functions, methods from linear algebra, partially ordered sets, polytopes, hyperplane arrangements, and matroids. Subsequent chapters illustrate applications of these methods for counting a wide array of objects.
The contributors for this book represent an international spectrum of researchers with strong histories of results. The chapters are organized so readers advance from the more general ones, namely enumeration methods, towards the more specialized ones.
Topics include coverage of asymptotic normality in enumeration, planar maps, graph enumeration, Young tableaux, unimodality, log-concavity, real zeros, asymptotic normality, trees, generalized Catalan paths, computerized enumeration schemes, enumeration of various graph classes, words, tilings, pattern avoidance, computer algebra, and parking functions.
Beneficial to a wide audience: experts interested in learning more about the finer points, general readers interested in the topic, and novices.
