Algorithmic and Enumerative Combinatorics

Algorithmic and Enumerative Combinatorics," as we understand it in this proposal, is the general research area which is defined by the interplay of the fields of Enumerative Combinatorics, Analytic Combinatorics, and Algorithmics. It is a very active research area, which, aside from the three fields fuelling each other mutually, receives as well constant impetus from outside, by its interaction with algebra, probability, statistical physics, and computer science. It is very modern as it necessarily requires skills in many different fields, and as it is unthinkable nowadays to make progress in this area without using (the) computer (algebra). The main subjects which define the "keywords" binding the interests of the project investigators of the proposed SFB are Enumeration of Combinatorial Structures, Analysis of Algorithms, Computer Algebra, Functional/Differential/Difference Equations, (Multiple) Summations and Integrals, Complex Asymptotics, Hypergeometrics, and Discrete Probability and Limiting Objects. The proposed SFB shall unite three research groups located at the Johannes Kepler University Linz, the University of Vienna, and the Vienna University of Technology, and it is divided into 8 scientific projects. All three research groups belong today to the leading research centres in Algorithmic and Enumerative Combinatorics on an international level. The aim of the proposed SFB is to join these forces and complementary skills to extend and support existing cooperations and to create new synergies. Major activities of the SFB will include a guest programme, the organization of annual workshops, and the organization of thematic schools. These workshops and schools will be open for researchers outside the SFB. One of the most important issues is to employ young researchers by this research project in order to give them a chance to proceed in their own scientific development. They should cooperate with several research groups within the SFB as well as get in contact with the international guests of the guest programme. Furthermore, they will profit from the workshops and schools organized within the SFB.