**by Mitchel T. Keller, William T. Trotter**

DescriptionTable of ContentsDetailsHashtagsReport an issue ### Book Description

Applied Combinatorics is an open-source book for a course covering the fundamental enumeration techniques (permutations, combinations, subsets, pigeon hole principle), recursion and mathematical induction, more advanced enumeration techniques (inclusion-exclusion, generating functions, recurrence relations, Polyá theory), discrete structures (graphs, digraphs, posets, interval orders), and discrete optimization (minimum weight spanning trees, shortest paths, network flows). There are also chapters introducing discrete probability, Ramsey theory, combinatorial applications of network flows, and a few other nuggets of discrete mathematics. ### Table of Contents

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This open book is licensed under a Creative Commons License (CC BY-SA). You can download Applied Combinatorics ebook for free in PDF format (7.5 MB).

Chapter 1

An Introduction to Combinatorics

Chapter 2

Strings, Sets, and Binomial Coefficients

Chapter 3

Induction

Chapter 4

Combinatorial Basics

Chapter 5

Graph Theory

Chapter 6

Partially Ordered Sets

Chapter 7

Inclusion-Exclusion

Chapter 8

Generating Functions

Chapter 9

Recurrence Equations

Chapter 10

Probability

Chapter 11

Applying Probability to Combinatorics

Chapter 12

Graph Algorithms

Chapter 13

Network Flows

Chapter 14

Combinatorial Applications of Network Flows

Chapter 15

Pólya's Enumeration Theorem

Chapter 16

The Many Faces of Combinatorics

Publisher

Self-publishing

Published

2017

Pages

393

Edition

1

Language

English

PDF Size

7.5 MB

License