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Combinatorics Through Guided Discovery
Kenneth P. Bogart
Contents
Index
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Annotations
Contents
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Front Matter
Colophon
Author Biography
Preface
Preface to PreTeXt edition
1
What is Combinatorics?
About These Notes
Basic Counting Principles
Some Applications of the Basic Principles
Supplementary Chapter Problems
2
Applications of Induction and Recursion in Combinatorics and Graph Theory
Some Examples of Mathematical Induction
Recurrence Relations
Graphs and Trees
Supplementary Problems
3
Distribution Problems
The idea of a distribution
Partitions and Stirling Numbers
Partitions of Integers
Supplementary Problems
4
Generating Functions
The Idea of Generating Functions
Generating functions for integer partitions
Generating Functions and Recurrence Relations
Supplementary Problems
5
The Principle of Inclusion and Exclusion
The size of a union of sets
Application of Inclusion and Exclusion
Deletion-Contraction and the Chromatic Polynomial
Supplementary Problems
6
Groups acting on sets
Permutation Groups
Groups Acting on Sets
Pรณlya-Redfield Enumeration Theory
Supplementary Problems
Back Matter
Relations
Mathematical Induction
Exponential Generating Functions
GNU Free Documentation License
Index
Authored in PreTeXt
Combinatorics Through Guided Discovery
Kenneth P. Bogart
Dartmouth College
Editors
Mitchel T. Keller
Washington & Lee University
Oscar Levin
University of Northern Colorado
Kent E. Morrison
American Institute of Mathematics
Colophon
Author Biography
Preface
Preface to PreTeXt edition