Applied Combinatorics

by Mitchel T. Keller, William T. Trotter

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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.

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).

Table of Contents

Chapter 1
An Introduction to Combinatorics
Chapter 2
Strings, Sets, and Binomial Coefficients
Chapter 3
Chapter 4
Combinatorial Basics
Chapter 5
Graph Theory
Chapter 6
Partially Ordered Sets
Chapter 7
Chapter 8
Generating Functions
Chapter 9
Recurrence Equations
Chapter 10
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

Book Details

PDF Size
7.5 MB

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