Hankel determinants of sums of consecutive weighted Schröder numbers

Sen Peng Eu, Tsai Lien Wong, Pei Lan Yen

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

We consider weighted large and small Schröder paths with up steps (1,1), down steps (1,-1) assigned the weight of 1 and with level steps (2,0) assigned the weight of t, where t is a real number. The weight of a path is the product of the weights of all its steps. Let rℓ(t) and sℓ(t) be the total weight of all weighted large and small Schröder paths from (0,0) to (2ℓ,0), respectively. For constants α, β, we derive the generating functions and the explicit formulae for the determinants of the Hankel matrices (αri+j-2(t)+βri+j-1(t))i,j=1n, (αri+j-1(t) +βri+j(t))i,j=1n, (αsi+j-2(t)+βsi+j-1(t))i,j=1n and (αsi+j-1(t)+βsi+j(t))i,j=1n combinatorially via suitable lattice path models.

Original languageEnglish
Pages (from-to)2285-2299
Number of pages15
JournalLinear Algebra and Its Applications
Volume437
Issue number9
DOIs
Publication statusPublished - 2012 Nov 1

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Keywords

  • Combinatorial methods
  • Hankel determinants
  • Non-intersecting lattice paths
  • Schröder numbers

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Numerical Analysis
  • Geometry and Topology
  • Discrete Mathematics and Combinatorics

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