250075 VO Selected Topics in Combinatorics (2005W)

An integer partition is a way of splitting a number n into integer parts. In general there are no explicit formulas for the number of partitions of n with certain properties. But these numbers can be characterized by their generating functions and we can find interesting bijections between different classes of partitions. E.g. Euler has proved that every number n has as many integer partitions into odd parts as into distinct parts. Starting with this theorem we give an elementary introduction to the theory of integer partitions.
Some highlights of the course are Euler¿s pentagonal number theorem, the q-binomial theorem, the triple product identity of Jacobi and the famous Rogers-Ramanujan identities.