NDLI: Zeilberger's holonomic ansatz for Pfaffians

Content Provider	ACM Digital Library
Author	Ishikawa, Masao Koutschan, Christoph
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.
Starting Page	227
Ending Page	233
Page Count	7
File Format	PDF
ISBN	9781450312691
DOI	10.1145/2442829.2442863
Language	English
Publisher	Association for Computing Machinery (ACM)
Publisher Date	2012-07-22
Publisher Place	New York
Access Restriction	Subscribed
Subject Keyword	Wz theory Pfaffian Determinant Motzkin number Computer proof Minor Symbolic summation Holonomic systems approach
Content Type	Text
Resource Type	Article

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Zeilberger's holonomic ansatz for Pfaffians