Cover 1
Title page 2
Contents 4
Preface 6
Notation 10
Fibonacci numbers, quickly 12
Fibonacci numbers, the formula 14
The clubs of Oddtown 16
Same-size intersections 18
Error-correcting codes 22
Odd distances 28
Are these distances Euclidean? 30
Packing complete bipartite graphs 34
Equiangular lines 38
Where is the triangle? 42
Checking matrix multiplication 46
Tiling a rectangle by squares 50
Three Petersens are not enough 52
Petersen, Hoffman–Singleton, and maybe 57 56
Only two distances 62
Covering a cube minus one vertex 66
Medium-size intersection is hard to avoid 68
On the difficulty of reducing the diameter 72
The end of the small coins 78
Walking in the yard 82
Counting spanning trees 88
In how many ways can a man tile a board? 96
More bricks—more walls? 108
Perfect matchings and determinants 118
Turning a ladder over a finite field 124
Counting compositions 130
Is it associative? 136
The secret agent and umbrella 142
Shannon capacity of the union: a tale of two fields 150
Equilateral sets 158
Cutting cheaply using eigenvectors 164
Rotating the cube 174
Set pairs and exterior products 182
Index 190
Back Cover 194