Applied Mathematics and Mechanics

, Volume 10, Issue 12, pp 1131–1135 | Cite as

On the lattice path method in convolution-type combinatorial identities (II)—The weighted counting function method on lattice paths

  • Chu Wen-chang
Article

Abstract

An independent method for paper [10]is presented. Weighted lattice paths are enumerated by counting function which is a natural extension of Gaussian multinomial coefficient in the case of unrestricted paths. Convolutions for path counts are investigated, which yields some Vandermunde-type identities for multinomial and q — multinomial coefficients.

Keywords

Mathematical Modeling Convolution Industrial Mathematic Function Method Natural Extension 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    Andrews, G. E.,The Theory of Partitions, Addison-Wesley, London (1976).Google Scholar
  2. [2]
    Bender, E. A., A binomialq — Vandermonde convolution,Discrete Math., 1 (1971), 115 - 119.Google Scholar
  3. [3]
    Carlitz, L., A note onq — Eulerian numbers,J. Comb. Th (A),25 (1978), 90 - 94.Google Scholar
  4. [4]
    Foukles, H. O., A non-recursive Combinatorial rule for Eulerian numbers,J. Comb. Th (A),22 (1977), 246 - 248.Google Scholar
  5. [5]
    Polya, G., On the number of certain lattice polytopes,J. Comb. Th.,6 (1969), 102 - 105.Google Scholar
  6. [6]
    Sulanke, R. A., A generalizedq — Vandermonde convolution,J. Comb. Th (A),31 (1981), 33 - 42.Google Scholar
  7. [7]
    Sulanke, R. A.,q — countingn — dimensional lattice paths,J. Comb. Th (A),33 (1982), 135 - 146.Google Scholar
  8. [8]
    Zeilberger, D., A lattice walk approach to the ‘inv’ and ‘maj’q — counting of multiset permutations,J. Math. Anal. and Appl.,74 (1980), 192 - 199.Google Scholar
  9. [9]
    Niederhausen, H., Linear recurrences under side conditions,Europ. J. Combinatorics, 1 (1980), 353 - 368.Google Scholar
  10. [10]
    Chu Wen-chang, On the lattice path method in convolution type combinatorial identities (I)—A family of Lebesque-Stieltjes integral identities,Dongbei Shuxue. 4, 2 (1988) 233 - 240. (in Chinese)Google Scholar

Copyright information

© Shanghai University of Technology 1989

Authors and Affiliations

  • Chu Wen-chang
    • 1
  1. 1.Institute of Systems ScienceAcademia SinicaBeijing

Personalised recommendations