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Probsolem solving method in combinatorics

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Cấu trúc

  • Cover

  • © 2013

  • Contents

  • Introduction

    • For the Student

  • 1: First Concepts

    • 1.1 Sets and First Countings

    • 1.2 Induction

    • 1.3 Paths in Boards

    • 1.4 A Couple of Tricks

    • 1.5 Problems

  • 2: The Pigeonhole Principle

    • 2.1 The Pigeonhole Principle

    • 2.2 Ramsey Numbers

    • 2.3 The Erdos-Szekeres Theorem

    • 2.4 An Application in Number Theory

    • 2.5 Problems

  • 3: Invariants

    • 3.1 Definition and First Examples

    • 3.2 Colorings

    • 3.3 Problems Involving Games

    • 3.4 Problems

  • 4: Graph Theory

    • 4.1 Basic Concepts

    • 4.2 Connectedness and Trees

    • 4.3 Bipartite Graphs

    • 4.4 Matchings

    • 4.5 Problems

  • 5: Functions

    • 5.1 Functions in Combinatorics

    • 5.2 Permutations

    • 5.3 Counting Twice

    • 5.4 The Erdos-Ko-Rado Theorem

    • 5.5 Problems

  • 6: Generating Functions

    • 6.1 Basic Properties

    • 6.2 Fibonacci Numbers

    • 6.3 Catalan Numbers

    • 6.4 The Derivative

    • 6.5 Evaluating Generating Functions

    • 6.6 Problems

  • 7: Partitions

    • 7.1 Partitions

    • 7.2 Stirling Numbers of the First Kind

    • 7.3 Stirling Numbers of the Second Kind

    • 7.4 Problems

  • 8: Hints for the Problems

    • 8.1 Hints for Chap. 1

    • 8.2 Hints for Chap. 2

    • 8.3 Hints for Chap. 3

    • 8.4 Hints for Chap. 4

    • 8.5 Hints for Chap. 5

    • 8.6 Hints for Chap. 6

    • 8.7 Hints for Chap. 7

  • 9: Solutions to the Problems

    • 9.1 Solutions for Chap. 1

    • 9.2 Solutions for Chap. 2

    • 9.3 Solutions for Chap. 3

    • 9.4 Solutions for Chap. 4

    • 9.5 Solutions for Chap. 5

    • 9.6 Solutions for Chap. 6

    • 9.7 Solutions for Chap. 7

  • Notation

  • Further Reading

  • Index

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