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
An Introduction to Combinatorics
Strings, Sets, and Binomial Coefficients
Partially Ordered Sets
Applying Probability to Combinatorics
Combinatorial Applications of Network Flows
Pólya's Enumeration Theorem
The Many Faces of Combinatorics