Masao Ishikawa, Christoph Koutschan,
"Zeilberger's Holonomic Ansatz for Pfaffians"
, in Joris von der Hoeven, Mark von Hoej: Proceedings of ISSAC 2012, ACM, Seite(n) 227-233, 2012, ISBN: 978-1-4503-1269
Zeilberger's Holonomic Ansatz for Pfaffians
Sprache des Titels:
Proceedings of ISSAC 2012
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.