Abstract
A variation of Zeilberger's holonomic ansatz for symbolic determinant evaluations is proposed which is tailored to deal with Pfaffians. The method is also applicable to determinants of skew-symmetric matrices, for which the original approach does not work. As Zeilberger's approach is based on the Laplace expansion (cofactor expansion) of the determinant, we derive our approach from the cofactor expansion of the Pfaffian. To demonstrate the power of our method, we prove, using computer algebra algorithms, some conjectures proposed in the paper "Pfaffian decomposition and a Pfaffian analogue of q-Catalan Hankel determinants" by Ishikawa, Tagawa, and Zeng. A minor summation formula related to partitions and Motzkin paths follows as a corollary.
| Original language | English |
|---|---|
| Title of host publication | Proceedings of ISSAC 2012 |
| Editors | Joris von der Hoeven, Mark von Hoej |
| Publisher | ACM |
| Pages | 227-233 |
| Number of pages | 7 |
| ISBN (Print) | 978-1-4503-1269 |
| Publication status | Published - 2012 |
Fields of science
- 101001 Algebra
- 101002 Analysis
- 101 Mathematics
- 102 Computer Sciences
- 102011 Formal languages
- 101009 Geometry
- 101013 Mathematical logic
- 101020 Technical mathematics
- 101025 Number theory
- 101012 Combinatorics
- 101005 Computer algebra
- 101006 Differential geometry
- 101003 Applied geometry
- 102025 Distributed systems
JKU Focus areas
- Computation in Informatics and Mathematics