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.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Andrews, G. E.,The Theory of Partitions, Addison-Wesley, London (1976).
Bender, E. A., A binomialq — Vandermonde convolution,Discrete Math., 1 (1971), 115 - 119.
Carlitz, L., A note onq — Eulerian numbers,J. Comb. Th (A),25 (1978), 90 - 94.
Foukles, H. O., A non-recursive Combinatorial rule for Eulerian numbers,J. Comb. Th (A),22 (1977), 246 - 248.
Polya, G., On the number of certain lattice polytopes,J. Comb. Th.,6 (1969), 102 - 105.
Sulanke, R. A., A generalizedq — Vandermonde convolution,J. Comb. Th (A),31 (1981), 33 - 42.
Sulanke, R. A.,q — countingn — dimensional lattice paths,J. Comb. Th (A),33 (1982), 135 - 146.
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.
Niederhausen, H., Linear recurrences under side conditions,Europ. J. Combinatorics, 1 (1980), 353 - 368.
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)
Author information
Authors and Affiliations
Additional information
Communicated by Wu Xue-mou
Rights and permissions
About this article
Cite this article
Wen-chang, C. On the lattice path method in convolution-type combinatorial identities (II)—The weighted counting function method on lattice paths. Appl Math Mech 10, 1131–1135 (1989). https://doi.org/10.1007/BF02016301
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02016301