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

Masao Ishikawa, Hiroyuki Tagawa, Jiang Zeng

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)


Motivated by the Hankel determinant evaluation of moment sequences, we study an analogous Pfaffian 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.

Original languageEnglish
Pages (from-to)1263-1284
Number of pages22
JournalJournal of Combinatorial Theory. Series A
Issue number6
Publication statusPublished - Aug 2013
Externally publishedYes


  • Hankel determinants
  • Moments of orthogonal polynomials
  • Pfaffian decomposition
  • Pfaffian of Catalan numbers
  • Shifted reverse plane partitions

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics
  • Computational Theory and Mathematics


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