Hankel determinants for generating functions of Catalan-like numbers. Issue 3 (4th March 2019)

• Record Type: Journal Article
• Authors: Liu, Lily Li; Mu, Lili
• Is Part Of: Linear & multilinear algebra. Volume 67:Issue 3(2019)
• Page Start: 499
• Page End: 509
• Publication Date: 2019-03-04
• Subjects: Hankel determinant -- orthogonal polynomial -- Catalan-like number; 15A15 -- 05A15 -- 42C05; Algebras, Linear -- Periodicals; Multilinear algebra -- Periodicals; 512.505
• DOI: 10.1080/03081087.2017.1422690
• Languages: English
• ISSNs: 0308-1087

Abstract

Abstract: LetR n ( x ) = ∑ i = 0 n r i x n - i be the generating functions of Catalan-like numbers( r n ) n ≥ 0 . We show that the corresponding Hankel determinantsdet [ R i + j ( x ) ] 0 ≤ i, j ≤ n satisfy a three-term recurrence relation. As applications, we express the Hankel determinants of some classical combinatorial counting coefficients, including the Catalan numbers, the central binomial coefficients, the large and little Schröder numbers, in a unified way.