A direct method for evaluating some nice Hankel determinants and proofs of several conjectures

DOI10.1016/j.laa.2012.10.050zbMath1263.15006OpenAlexW2014030600WikidataQ123289722 ScholiaQ123289722MaRDI QIDQ1938709

Xing-Biao Hu, Ying-Nan Zhang, Xiang-Ke Chang

Publication date: 22 February 2013

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.laa.2012.10.050

zbMATH Keywords

Hankel determinantCatalan numbersMotzkin numbersSchröder numbers

Mathematics Subject Classification ID

Exact enumeration problems, generating functions (05A15) Determinants, permanents, traces, other special matrix functions (15A15) Special sequences and polynomials (11B83)

Related Items

Hankel determinants and shifted periodic continued fractions ⋮ Combinatorial proofs of addition formulas

Cites Work

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• Hankel determinants of sums of consecutive weighted Schröder numbers
• Some determinants of path generating functions
• Hankel determinants of sums of consecutive Motzkin numbers
• Determinantal identities: Gauss, Schur, Cauchy, Sylvester, Kronecker, Jacobi, Binet, Laplace, Muir, and Cayley
• Determinants of (generalised) Catalan numbers
• Binomial determinants, paths, and hook length formulae
• Advanced determinant calculus
• Catalan-like numbers and determinants
• A determinant property of Catalan numbers
• Hankel determinants for some common lattice paths
• Aztec diamonds and digraphs, and Hankel determinants of Schröder numbers
• The generating function of ternary trees and continued fractions
• Advanced determinant calculus: a complement
• Motzkin numbers