Combinatorics is the branch of mathematics that deals with determining the number of ways to arrange things, the number of subsets of a set that have a certain property, etc.

The two fundamental concepts in combinatorics are permutations and combinations.

A permutation is an arrangement of a set of objects, or specifically an arrangement of a subset of a certain size of some set of objects.

A combination is a subset of a certain size of some set of objects, without regard to their order.

These concepts are inherent to some kinds of probability problems.

It is a standard technique in mathematics to reduce a problem that you care deeply about to a problem in combinatorics, i.e. to questions about arranging finitely many objects. The resulting combinatorial yoga can be difficult and diverting in its own right but the real interest comes from the original problem be it in Lie groups or probability or whatever.

For this reason Noether has always felt that studying combinatorics for its own sake is a bit like sex without love.

This is a starting point for anyone interested in the field of combinatorics. It's definitely one of my favorite facets of pure math, and I'll slowly be noding all the definitions. I've done some already, and I'll post a few a day untill I've noded everything on this list. In the meantime, I'll have added other hard-links, so I guess I'll never finish. But it's a start.

see also:

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