Combinatorics is a subject of increasing importance because of its links with computer science, statistics,
and algebra. This textbook stresses common techniques (such as generating functions and recursive construction)
that underlie the great variety of subject matter, and the fact that a constructive or algorithmic proof is more
valuable than an existence proof. The author emphasizes techniques as well as topics and includes many algorithms
described in simple terms. The text should provide essential background for students in all parts of discrete mathematics.
Table of Contents
What is combinatorics?
On numbers and counting
Subsets, partitions, permutations
Recurrence relations and generating functions
The Principle of Inclusion and Exclusion
Latin squares and SDRs
Extremal set theory
Steiner triple systems
Finite geometry
Ramsey's theorem
Graphs
Posets, lattices and matroids
More on partitions and permutations
Automorphism groups and permutation groups
Enumeration under group action
Designs
Error-correcting codes
Graph colourings
The infinite
Where to from here?
