Algorithmic Combinatorics at RISC
The Current Team
Prof. Peter Paule (team leader, Austria), Dr. Stefan Gerhold (PostDoc, Austria), Dr. Ralf Hemmecke (PostDoc, Germany), Dr. Manuel Kauers (PostDoc, Germany), Dr. Axel Riese (PostDoc, Austria), Dr. Carsten Schneider (PostDoc, Germany), DI Cleo Pau (PhD student, Romania), DI Veronika Pillwein (PhD student, Austria), Mag. Burkhard Zimmermann (PhD student, Austria), Martin Semrad (diploma student, Austria), and Robert Wiesinger (diploma student, Austria).
The RISC Combinatorics Group (October 2004) —
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From left to right: M. Kauers, R. Hemmecke, J.M. Garcia Vallinas,
P. Paule, A. Riese, C. Pau, B. Zimmermann, C. Schneider
Research Interests
We are mainly interested in the connection of classical combinatorics, special functions, and computer algebra ("symbolic computation in combinatorics"). Currently, special emphasis is put on symbolic summation and special function identities. The overall object is the development of new algorithms and tools (computer algebra software) which assist practical problem solving in mathematics, but also in mathematical chemistry (e.g., counting molecular configurations), computer science (e.g., analysis of algorithms), physics (e.g., statistical mechanics), engineering (e.g., manipulation of special functions), and computer simulation (e.g., finite element method).
Finite Elements |
Partition Analysis |
Software
The software produced by the RISC combinatorics group has found many users from all over the world. It is freely available via the web; since June 1999 several hundred requests have been documented. Moreover, leading mathematicians refer to the software in their talks:
D. Zeilberger at Minneapolis
Projects
The National Institute of Standards and Technology (NIST, Gaithersburg, USA) currently pursues the project of a new and strongly updated version of the classic "Handbook of Mathematical Functions" (Abramowitz & Stegun, 1964). Prof. Paule has been invited to serve as editor for the new section on computer algebra.The RISC combinatorics group is member of the special research action Numerical and Symbolic Scientific Computing (SFB, sponsored by the Austrian Science Foundation FWF).
There are intense international scientific cooperations, for instance, with Prof. George E. Andrews (PennState, USA), with the Algorithms Project at INRIA-Paris (Dr. F. Chyzak), and with Prof. Volker Strehl (Erlangen, Germany).
Some members of the RISC combinatorics group have received international grants, e.g., F. Caruso ("Borsa di Studio per Corsi di Specializazione all'Esteero" of the University of Catania, Italy), C. Schneider and M. Kauers (DAAD, Germany).