Hankel determinants of sums of consecutive weighted Schröder numbers

Sen Peng Eu*, Tsai Lien Wong, Pei Lan Yen

*此作品的通信作者

研究成果: 雜誌貢獻期刊論文同行評審

5 引文 斯高帕斯(Scopus)

摘要

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.

原文英語
頁(從 - 到)2285-2299
頁數15
期刊Linear Algebra and Its Applications
437
發行號9
DOIs
出版狀態已發佈 - 2012 十一月 1

ASJC Scopus subject areas

  • 代數與數理論
  • 數值分析
  • 幾何和拓撲
  • 離散數學和組合

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