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Combinatorics Through Guided Discovery
This book is an introduction to combinatorial mathematics, also known as combinatorics. The book focuses especially but not exclusively on the part of combinatorics that mathematicians refer to as “counting.” The book consists almost entirely of problems. Some of the problems are designed to lead you to think about a concept, others are designed to help you figure out a concept and state a theorem about it, while still others ask you to prove the theorem.
- Author
- Kenneth P. Bogart
- Publisher
- Dartmouth University
- Source
- LibreTexts
- License
- GNU FDL
- Language
- EN
- Category
- Basic Sciences
Contents· 30 sections
- 01: What is Combinatorics
- 1.01: About These Notes
- 1.02: Basic Counting Principles
- 1.03: Some Applications of Basic Counting Principles
- 1.04: What is Combinatorics (Exercises)
- 02: Induction and Recursion
- 2.01: Some Examples of Mathematical Introduction
- 2.02: Recurrence Relations
- 2.03: Graph and Trees
- 2.04: Applications of Induction and Recursion in Combinatorics and Graph Theory (Exercises)
- 03: Distribution Problems
- 3.01: The Idea of Distribution
- 3.02: Partitions and Stirling Numbers
- 3.03: Partitions of Integers
- 3.04: Distribution Problems (Exercises)
- 04: Generating Functions
- 4.01: The Idea of Generating Functions
- 4.02: Generating Functions for Integer Partitions
- 4.03: Generating Functions and Recurrence Relations
- 4.04: Generating Functions (Exercises)
- 05: The Principle of Inclusion and Exclusion
- 5.01: The Size of a Union of Sets
- 5.02: Applications of Inclusion and Exclusion
- 5.03: Deletion-Contraction and the Chromatic Polynomial
- 5.04: The Principle of Inclusion and Exclusion (Exercises)
- 06: Groups Acting on Sets
- 6.01: Permutation Groups
- 6.02: Groups Acting on Sets
- 6.03: Polya-Redfield Enumeration Theory
- 6.04: Groups Acting on Sets (Exercises)