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

Masao Ishikawa, Hiroyuki Tagawa, Jiang Zeng

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

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
Volume120
Issue number6
DOIs
Publication statusPublished - Aug 2013
Externally publishedYes

Fingerprint

Hankel Determinant
Pfaffian
Analogue
Decomposition
Decompose
Moment Sequence
Polynomials
Plane Partitions
Skew symmetric matrix
LU decomposition
Classical Orthogonal Polynomials
Product formula
Evaluation
Enumeration
Reverse
Evaluate

Keywords

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

ASJC Scopus subject areas

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

Cite this

Pfaffian decomposition and a Pfaffian analogue of q-Catalan Hankel determinants. / Ishikawa, Masao; Tagawa, Hiroyuki; Zeng, Jiang.

In: Journal of Combinatorial Theory - Series A, Vol. 120, No. 6, 08.2013, p. 1263-1284.

Research output: Contribution to journalArticle

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