|Papers and Preprints||The Combinatorics Seminar|
Instructions for applying for these positions can be found here. Observe that the Swedish node of the network is administered from Linköping, but if you are interested in a post/pre-doc position in Göteborg, you should contact Einar Steingrimsson (in addition to sending a formal application as instructed here.)
The department has strong groups in many fields, including algebra, mathematical statistics/probability and optimization (see here).
|Niklas Eriksen||Anders Claesson||Einar Steingrímsson|
|Sergey Kitaev||Toufik Mansour||Petter Brändén||Antoine Vella|
The naive answer is that combinatorics is a theory of counting discrete objects, in particular, counting the elements of a finite set. However, we aren't always interested in the actual numbers of the objects being counted but rather in showing that two sets of apparently different objects are in fact equal in size.
In such a situation, one usually looks for a bijection between the two sets and such a bijection should explain why the two sets are equinumerous. That is, the bijection should reveal a structure common to the two sets. In this sense, bijections are to enumerative combinatorics what homomorphisms are to group theory, or homeomorphisms to topology, namely tools to discern an underlying structure. Look here for some simple examples of such questions in combinatorics. Here is an interesting survey article on combinatorics by Anders Björner and Richard P. Stanley. (Also here.)
Combinatorics has close relations to many other fields of mathematics, such as optimization, topology, algebra and algebraic geometry and even to physics. While combinatorics can often be seen as an aid in optimization theory, it is more frequently on the receiving end with respect to topology and algebra. In fact, many significant discoveries in combinatorics of the last few decades have been made with tools from these fields.