A Pfaffian analogue of the Hankel determinants and the Selberg integrals (Topics in Combinatorial Representation Theory)
A Pfaffian analogue of the Hankel determinants and the Selberg integrals (Topics in Combinatorial Representation Theory)
复制标题
汉克尔行列式和塞尔伯格积分的普法夫类似物（组合表示理论主题）
DOI：
10.1145/2442829.2442863
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发表时间：
2012
影响因子：
5.9
通讯作者：
Jiang Zeng
中科院分区：
文献类型：
--
作者：
石川 雅雄;Jiang Zeng
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 ofq-Catalan Hankel determinants" by Ishikawa, Tagawa, and Zeng. A minor summation formula related to partitions and Motzkin paths follows as a corollary.
