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Author: Alan Tucker
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 472
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Book Description
"T. 1. Graph Theory. 1. Ch. 1. Elements of Graph Theory. 3. Ch. 2. Covering Circuits and Graph Coloring. 53. Ch. 3. Trees and Searching. 95. Ch. 4. Network Algorithms. 129. Pt. 2. Enumeration. 167. Ch. 5. General Counting Methods for Arrangements and Selections. 169. Ch. 6. Generating Functions. 241. Ch. 7. Recurrence Relations. 273. Ch. 8. Inclusion-Exclusion. 309. Pt. 3. Additional Topics. 341. Ch. 9. Polya's Enumeration Formula. 343. Ch. 10. Games with Graphs. 371. . Appendix. 387. . Glossary of Counting and Graph Theory Terms. 403. . Bibliography. 407. . Solutions to Odd-Numbered Problems. 409. . Index. 441.
Author: Alan Tucker
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 472
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Book Description
"T. 1. Graph Theory. 1. Ch. 1. Elements of Graph Theory. 3. Ch. 2. Covering Circuits and Graph Coloring. 53. Ch. 3. Trees and Searching. 95. Ch. 4. Network Algorithms. 129. Pt. 2. Enumeration. 167. Ch. 5. General Counting Methods for Arrangements and Selections. 169. Ch. 6. Generating Functions. 241. Ch. 7. Recurrence Relations. 273. Ch. 8. Inclusion-Exclusion. 309. Pt. 3. Additional Topics. 341. Ch. 9. Polya's Enumeration Formula. 343. Ch. 10. Games with Graphs. 371. . Appendix. 387. . Glossary of Counting and Graph Theory Terms. 403. . Bibliography. 407. . Solutions to Odd-Numbered Problems. 409. . Index. 441.
Author: Fred Roberts
Publisher: CRC Press
ISBN: 1420099833
Category : Computers
Languages : en
Pages : 889
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Book Description
Now with solutions to selected problems, Applied Combinatorics, Second Edition presents the tools of combinatorics from an applied point of view. This bestselling textbook offers numerous references to the literature of combinatorics and its applications that enable readers to delve more deeply into the topics.After introducing fundamental counting
Author: M. Lothaire
Publisher: Cambridge University Press
ISBN: 9780521848022
Category : Computers
Languages : en
Pages : 646
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Book Description
Publisher Description
Author: Edward A. Bender
Publisher: Courier Corporation
ISBN: 0486151506
Category : Mathematics
Languages : en
Pages : 789
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Book Description
This introduction to combinatorics, the foundation of the interaction between computer science and mathematics, is suitable for upper-level undergraduates and graduate students in engineering, science, and mathematics. The four-part treatment begins with a section on counting and listing that covers basic counting, functions, decision trees, and sieving methods. The following section addresses fundamental concepts in graph theory and a sampler of graph topics. The third part examines a variety of applications relevant to computer science and mathematics, including induction and recursion, sorting theory, and rooted plane trees. The final section, on generating functions, offers students a powerful tool for studying counting problems. Numerous exercises appear throughout the text, along with notes and references. The text concludes with solutions to odd-numbered exercises and to all appendix exercises.
Author: George Pólya
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 640
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Book Description
Author: Philippe Flajolet
Publisher: Cambridge University Press
ISBN: 1139477161
Category : Mathematics
Languages : en
Pages : 825
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Book Description
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: Richard P. Stanley
Publisher: Springer Science & Business Media
ISBN: 1461469988
Category : Mathematics
Languages : en
Pages : 226
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Book Description
Written by one of the foremost experts in the field, Algebraic Combinatorics is a unique undergraduate textbook that will prepare the next generation of pure and applied mathematicians. The combination of the author’s extensive knowledge of combinatorics and classical and practical tools from algebra will inspire motivated students to delve deeply into the fascinating interplay between algebra and combinatorics. Readers will be able to apply their newfound knowledge to mathematical, engineering, and business models. The text is primarily intended for use in a one-semester advanced undergraduate course in algebraic combinatorics, enumerative combinatorics, or graph theory. Prerequisites include a basic knowledge of linear algebra over a field, existence of finite fields, and group theory. The topics in each chapter build on one another and include extensive problem sets as well as hints to selected exercises. Key topics include walks on graphs, cubes and the Radon transform, the Matrix–Tree Theorem, and the Sperner property. There are also three appendices on purely enumerative aspects of combinatorics related to the chapter material: the RSK algorithm, plane partitions, and the enumeration of labeled trees. Richard Stanley is currently professor of Applied Mathematics at the Massachusetts Institute of Technology. Stanley has received several awards including the George Polya Prize in applied combinatorics, the Guggenheim Fellowship, and the Leroy P. Steele Prize for mathematical exposition. Also by the author: Combinatorics and Commutative Algebra, Second Edition, © Birkhauser.
Author: Fred S. Roberts
Publisher: CRC Press
ISBN: 1040120296
Category : Mathematics
Languages : en
Pages : 757
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Book Description
The third edition of this popular text presents the tools of combinatorics for a first undergraduate course. After introducing fundamental counting rules, tools of graph theory and relations, the focus is on three basic problems of combinatorics: counting, existence, and optimization problems.
Author: Nicholas Loehr
Publisher: CRC Press
ISBN: 149878027X
Category : Mathematics
Languages : en
Pages : 849
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Book Description
Combinatorics, Second Edition is a well-rounded, general introduction to the subjects of enumerative, bijective, and algebraic combinatorics. The textbook emphasizes bijective proofs, which provide elegant solutions to counting problems by setting up one-to-one correspondences between two sets of combinatorial objects. The author has written the textbook to be accessible to readers without any prior background in abstract algebra or combinatorics. Part I of the second edition develops an array of mathematical tools to solve counting problems: basic counting rules, recursions, inclusion-exclusion techniques, generating functions, bijective proofs, and linear algebraic methods. These tools are used to analyze combinatorial structures such as words, permutations, subsets, functions, graphs, trees, lattice paths, and much more. Part II cover topics in algebraic combinatorics including group actions, permutation statistics, symmetric functions, and tableau combinatorics. This edition provides greater coverage of the use of ordinary and exponential generating functions as a problem-solving tool. Along with two new chapters, several new sections, and improved exposition throughout, the textbook is brimming with many examples and exercises of various levels of difficulty.
Author: Michael Townsend
Publisher: Benjamin-Cummings Publishing Company
ISBN:
Category : Mathematics
Languages : en
Pages : 416
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Book Description
