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Place: Seminarraum Schloss Hagenberg
| 12.10. | Peter Paule (9:30, UFO) | Organizational items |
| Gabor Kusper | On the SAT problem (Part I) | |
| 17.10. | Axel Riese | qNormal - A Procedure for Normalizing Rational Functions
Abstract: We describe an efficient algorithm for identifying factors of the form 1 - qn in rational functions from Q(q). |
| 24.10. | Gabor Kusper | On the SAT problem (Part II) |
| Burki Zimmermann | Quasi-Polynomials (Part I) | |
| 31.10. | canceled | |
| 07.11. | Carsten Schneider | How one can play with sums |
| Burki Zimmermann | Quasi-Polynomials (Part II) | |
| 14.11. | Burki Zimmermann (Gemeindesaal) | Quasi-Polynomials (Part III) |
| 21.11. | Fabrizio Caruso | "Gosper-bijections" over shifted finite integer intervals with holes (Part I) |
| 28.11. | Fabrizio Caruso | "Gosper-bijections" over shifted finite integer intervals with holes (Part II) |
| 05.12. | Fabrizio Caruso | "Gosper-bijections" over shifted finite integer intervals with holes (Part III) |
| Robert Wiesinger | Linear recurrences with constant coefficients: the multivariate case (Part I) | |
| 12.12. | Robert Wiesinger | Linear recurrences with constant coefficients: the multivariate case (Part II) |
| 09.01. | Robert Wiesinger | Linear recurrences with constant coefficients: the multivariate case (Part III) |
| Axel Riese | Software news | |
| 16.01. | Erich Neuwirth | Extending Galton's board: Recursive combinatorial functions and Linear Algebra
Abstract: We will study recursively defined functions of the type F(n,k) = a(n-1,k) F(n-1,k) + b(n-1,k-1) F(n-1,k-1), which will be called Galton arrays with generators a(n,k) and b(n,k). Galton schemes can be seen as infinite triangular matrices, and therefore we can ask the question if the generators of a matrix product can be obtained through simple operations from the generators of the factors. Additionally, results about generators of the identity matrix can be used to derive inversion results about Galton schemes. Our general theorems unify many known results about Binomial coefficients, Stirling numbers, and similar well known combinatorial functions, and in particular many of the inversion results about these functions turn out to be special cases of our general approach. Our results are, however, more general. They also allow decomposition of certain Galton schemata into matrix products of simpler structures. Somewhat surprisingly, the proof techniques are mainly applications of elementary linear algebra methods. |
| 23.01. | Martin Semrad | Integer relations (Part I) |
| 30.01. | Martin Semrad | Integer relations (Part II) |