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Index
Cover page
Halftitle page
Series page
Title page
Copyright page
Contents
List of illustrations
List of tables
1 What is combinatorics?
2 Four types of problem
Existence problems
Construction problems
Enumeration problems
Optimization problems
The efficiency of algorithms
3 Permutations and combinations
Ordered selections
Unordered selections
Distributions
Winning the lottery
4 A combinatorial zoo
The box principle
Inclusion and exclusion
Derangements
The Tower of Hanoi
Poetry, pavings, and rabbits
Job assignments and marriage
Generators and enumerators
The game of Scrabble
Counting chessboards
5 Tilings and polyhedra
Tilings
Polyhedra
6 Graphs
What is a graph?
Trees
Eulerian and Hamiltonian graphs
Planar graphs
The missing region
The four-colour theorem
7 Square arrays
Magic squares
Latin squares
Orthogonal latin squares
8 Designs and geometry
Block designs
Triple systems
Finite projective planes
Tying things together
9 Partitions
Enter Euler
Enter Hardy and Ramanujan
Further reading
Index
Social media
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