Handbook of Enumerative Combinatorics Discrete Mathematics and Its Applications Series

Presenting the state of the art, the 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.

This important new work is edited by Miklós Bóna of the University of Florida where he is a member of the Academy of Distinguished Teaching Scholars. He received his Ph.D. in mathematics at Massachusetts Institute of Technology 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 for CRC Press/Chapman and Hall.

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.

This book will be beneficial to a wide audience. It will appeal to experts on the topic interested in learning more about the finer points, readers interested in a systematic and organized treatment of the topic, and novices who are new to the field.

Methods. Algebraic and Geometric Methods in Enumerative Combinatorics. Analytic Methods. Topics. Asymptotic Normality in Enumeration. Trees. Planar maps. Graph Enumeration. Unimodality, Log-Concavity, Real–Rootedness and Beyond. Words. Tilings. Lattice Path Enumeration. Catalan Paths and q; t-enumeration. Permutation Classes. Parking Functions. Standard Young Tableaux. Computer Algebra.

Miklós Bóna received his Ph.D. in mathematics at Massachusetts Institute of Technology in 1997. Since 1999, he has taught at the University of Florida, where in 2010 he was inducted in the Academy of Distinguished Teaching Scholars. He is the author of four books and more than 65 research articles, mostly focusing on enumerative and analytic combinatorics. His book Combinatorics of Permutations won the Outstanding Title Award from Choice, the journal of the American Library Association. He has mentored numerous graduate and undergraduate students. Miklós Bóna is an editor-in-chief for the Electronic Journal of Combinatorics, and for two book series at CRC Press.