[PDF] Generating Functionology eBook

Author : Herbert S. Wilf
Publisher : Elsevier
Page : 193 pages
File Size : 31,76 MB
Release : 2014-05-10
Category : Mathematics
ISBN : 1483276635

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Generatingfunctionology provides information pertinent to generating functions and some of their uses in discrete mathematics. This book presents the power of the method by giving a number of examples of problems that can be profitably thought about from the point of view of generating functions. Organized into five chapters, this book begins with an overview of the basic concepts of a generating function. This text then discusses the different kinds of series that are widely used as generating functions. Other chapters explain how to make much more precise estimates of the sizes of the coefficients of power series based on the analyticity of the function that is represented by the series. This book discusses as well the applications of the theory of generating functions to counting problems. The final chapter deals with the formal aspects of the theory of generating functions. This book is a valuable resource for mathematicians and students.

Author : Herbert S. Wilf
Publisher : Elsevier
Page : 239 pages
File Size : 41,91 MB
Release : 2013-10-22
Category : Mathematics
ISBN : 0080571514

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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. Provides new applications on the cycle index of the symmetric group, permutations and square roots, counting polyominoes, and exact covering sequences Features an Appendix on using MAPLE(r) and Mathematica (r) to generate functions Includes many new exercises with complete solutions at the end of each chapter

Author : Robert M. Young
Publisher : Cambridge University Press
Page : 436 pages
File Size : 11,87 MB
Release : 1992
Category : Mathematics
ISBN : 9780883853177

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This book explores the interplay between the two main currents of mathematics, the continuous and the discrete.

Author : Philippe Flajolet
Publisher : Cambridge University Press
Page : 825 pages
File Size : 45,29 MB
Release : 2009-01-15
Category : Mathematics
ISBN : 1139477161

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Analytic combinatorics aims to enable precise quantitative predictions of the properties of large combinatorial structures. The theory has emerged over recent decades as essential both for the analysis of algorithms and for the study of scientific models in many disciplines, including probability theory, statistical physics, computational biology, and information theory. With a careful combination of symbolic enumeration methods and complex analysis, drawing heavily on generating functions, results of sweeping generality emerge that can be applied in particular to fundamental structures such as permutations, sequences, strings, walks, paths, trees, graphs and maps. This account is the definitive treatment of the topic. The authors give full coverage of the underlying mathematics and a thorough treatment of both classical and modern applications of the theory. The text is complemented with exercises, examples, appendices and notes to aid understanding. The book can be used for an advanced undergraduate or a graduate course, or for self-study.

Author : Marko Petkovsek
Publisher : CRC Press
Page : 231 pages
File Size : 11,62 MB
Release : 1996-01-01
Category : Mathematics
ISBN : 1439864500

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This book is of interest to mathematicians and computer scientists working in finite mathematics and combinatorics. It presents a breakthrough method for analyzing complex summations. Beautifully written, the book contains practical applications as well as conceptual developments that will have applications in other areas of mathematics.From the ta

Author : László Lovász
Publisher : Springer Science & Business Media
Page : 344 pages
File Size : 47,76 MB
Release : 2006-05-10
Category : Mathematics
ISBN : 0387217770

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Aimed at undergraduate mathematics and computer science students, this book is an excellent introduction to a lot of problems of discrete mathematics. It discusses a number of selected results and methods, mostly from areas of combinatorics and graph theory, and it uses proofs and problem solving to help students understand the solutions to problems. Numerous examples, figures, and exercises are spread throughout the book.

Author : Herbert S Wilf
Publisher : Courier Corporation
Page : 304 pages
File Size : 24,16 MB
Release : 2013-01-18
Category : Mathematics
ISBN : 0486153347

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Topics include vector spaces and matrices; orthogonal functions; polynomial equations; asymptotic expansions; ordinary differential equations; conformal mapping; and extremum problems. Includes exercises and solutions. 1962 edition.

Author : Jonathan L. Gross
Publisher : CRC Press
Page : 664 pages
File Size : 23,13 MB
Release : 2016-04-19
Category : Computers
ISBN : 1584887443

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Combinatorial Methods with Computer Applications provides in-depth coverage of recurrences, generating functions, partitions, and permutations, along with some of the most interesting graph and network topics, design constructions, and finite geometries. Requiring only a foundation in discrete mathematics, it can serve as the textbook in a combinat

Author : Charles C Pinter
Publisher : Courier Corporation
Page : 402 pages
File Size : 34,73 MB
Release : 2010-01-14
Category : Mathematics
ISBN : 0486474178

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Accessible but rigorous, this outstanding text encompasses all of the topics covered by a typical course in elementary abstract algebra. Its easy-to-read treatment offers an intuitive approach, featuring informal discussions followed by thematically arranged exercises. This second edition features additional exercises to improve student familiarity with applications. 1990 edition.