%0 Journal Article
%T Pfaffian decomposition and a Pfaffian analogue of q-Catalan Hankel determinants
%A Masao Ishikawa
%A Hiroyuki Tagawa
%A Jiang Zeng
%J Mathematics
%D 2010
%I arXiv
%X 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.
%U http://arxiv.org/abs/1011.5941v1