O'Reilly logo

Combinatorics by Peter J. Cameron

Stay ahead with the world's most comprehensive technology and business learning platform.

With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, tutorials, and more.

Start Free Trial

No credit card required

1.  What is Combinatorics?

Combinatorics is the slums of topology.

J. H. C. Whitehead (attr.)1

I have to admit that he was not bad at combinatorial analysis — a branch, however, that even then I considered to be dried up.

Stanislaw Lem, His Master’s Voice (1968)

Combinatorics is special. Most mathematical topics which can be covered in a lecture course build towards a single, well-defined goal, such as Cauchy’s Theorem or the Prime Number Theorem. Even if such a clear goal doesn’t exist, there is a sharp focus (finite groups, perhaps, or non-parametric statistics). By contrast, combinatorics appears to be a collection of unrelated puzzles chosen at random.

Two factors contribute to this. First, combinatorics is broad rather than deep. Its tentacles ...

With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, interactive tutorials, and more.

Start Free Trial

No credit card required