250424 VO Selected topics in combinatorics (2006S)

q-identities are playing an increasing role in different parts of mathematics and physics (e.g. in combinatorics, in the theory of special functions and in quantum theory). In this course I want to study such aspects which do not need the theory of basic hypergeometric functions, such as q-analogs of classical identities (i.e. identities depending on an additional parameter q, which for q=1 reduce to these classical identities) and their relatives. Among other things we want to study q-analogs of the binomial theorem, of Taylor¿s theorem, of the exponential function, of Fibonacci, Stirling and Catalan numbers and some famous identities such as Euler¿s pentagonal number theorem, Jacobi¿s triple product identity and the identities of Rogers-Ramanujan.

The only prerequisite is familiarity with the content of the course Discrete Mathematics, especially with formal power series. I am preparing lecture notes which may be downloaded from my homepage. The first two chapters are already written. The rest will be added at due time. There is also the possibility to write a diploma thesis on this subject.