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 Miklos Bona 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.
Miklos is the author of four books and more than 65 research
articles, including the award-winning Combinatorics of
Permutations. Miklos Bona 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.
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