250027 VO Combinatorics (2009S)

Combinatorics, in its simplest form, deals with the enumeration of elements of a finite set. The most frequent basic combinatorial objects
are permutations, rearrangements, lattice paths, trees and graphs. The appeal of combinatorics comes from the fact that there is no uniform approach for the treatment of the different problems, but many different methods, each of which providing a conceptual approach to a particular type of problem, respectively shedding light on these problems from different angles. The fact that there are no limitations on imagination in combinatorics has given a boost to this area in the past. In particular, the interrelations to other areas, such as theory of finite groups, representation theory, commutative algebra, algebraic geometry, computer science, and statistical physics, became more and more
important.

This course will build on the material of the course "Diskrete Mathematik". Some topics from there will be treated here in a more profound manner, and there will be new topics, to be precise:

1. Combinatorial structures and their generating functions
2. Pölya theory and the enumeration of objects with symmetries
3. Methods for asymptotic enumeration
4. Combinatorial theory of partielly ordered sets