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arXiv · 1011.5941

Pfaffian decomposition and a Pfaffian analogue of q-Catalan Hankel determinants

Masao Ishikawa·Hiroyuki Tagawa·Jiang Zeng
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Abstract

Motivated by the Hankel determinant evaluation of moment sequences, we study a kind of Pfaffian analogue evaluation. We prove an LU-decomposition analogue for skew-symmetric matrices, called Pfaffian decomposition. We then apply this formula to evaluate Pfaffians related to some moment sequences of classical orthogonal polynomials. In particular we obtain a product formula for a kind of q-Catalan Pfaffians. We also establish a connection between our Pfaffian formulas and certain weighted enumeration of shifted reverse plane partitions.

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Masao Ishikawa, Hiroyuki Tagawa, Jiang Zeng. 2010-11-27. Pfaffian decomposition and a Pfaffian analogue of q-Catalan Hankel determinants. https://arxiv.org/abs/1011.5941

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