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Applied Combinatorics, 6th Edition

Alan Tucker

ISBN: 978-1-118-32451-6 January 2012 496 Pages

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Description

The new 6th edition of Applied Combinatorics builds on the previous editions with more in depth analysis of computer systems in order to help develop proficiency in basic discrete math problem solving. As one of the most widely used books in combinatorial problems, this edition explains how to reason and model combinatorically while stressing the systematic analysis of different possibilities, exploration of the logical structure of a problem, and ingenuity. Although important uses of combinatorics in computer science, operations research, and finite probability are mentioned, these applications are often used solely for motivation. Numerical examples involving the same concepts use more interesting settings such as poker probabilities or logical games.
Prelude.

Part One: Graph Theory.

Chapter 1: Elements of Graph Theory.

Chapter 2: Covering Circuits and Graph coloring.

Chapter 3: Trees and Searching.

Chapter 4: Network Algorithms.

Part Two: Enumeration.

Chapter 5: General Counting Methods for Arrangements and Selections.

Chapter 6: Generating Functions.

Chapter 7: Recurrence Relations.

Chapter 8: Inclusion-Exclusion.

Part Three: Additional Topics.

Chapter 9: Polya's Enumeration Formula.

Chapter 10: Games with Grapes.

Postlude.

Appendix.

  • This new sixth edition has new examples, expanded discussions, and additional exercises throughout the text.
  • A closing postlude about crytoanalysis has been added.
  • A greater emphasis on underlying reasoning in combinatorial problem-solving has been stressed throughout the text.


  • Theory is always first motivated by examples, and proofs are given only when their reasoning is needed to solve applied problems. Elsewhere, results are stated without proof, such as the form of solutions to various recurrence relations, and then applied in problem solving.
  • This new sixth edition has new examples, expanded discussions, and additional exercises throughout the text.