q-Counting n-dimensional lattice paths

Robert A. Sulanke

doi:10.1016/0097-3165(82)90002-4

q-Counting n-dimensional lattice paths

Robert A. Sulanke

Mathematics Department

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

Abstract

n-dimensional lattice paths are enumerated by generating functions which are Gaussian multinomial coefficients in the case of unrestricted paths. Convolutions for path counts are studied which yield a q-Vandermonde convolution and a determinant of Gaussian multinomial coefficients as the generating function for certain restricted paths.

Original language	English
Pages (from-to)	135-146
Number of pages	12
Journal	Journal of Combinatorial Theory, Series A
Volume	33
Issue number	2
DOIs	https://doi.org/10.1016/0097-3165(82)90002-4
State	Published - Sep 1982

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title = "q-Counting n-dimensional lattice paths",

abstract = "n-dimensional lattice paths are enumerated by generating functions which are Gaussian multinomial coefficients in the case of unrestricted paths. Convolutions for path counts are studied which yield a q-Vandermonde convolution and a determinant of Gaussian multinomial coefficients as the generating function for certain restricted paths.",

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AB - n-dimensional lattice paths are enumerated by generating functions which are Gaussian multinomial coefficients in the case of unrestricted paths. Convolutions for path counts are studied which yield a q-Vandermonde convolution and a determinant of Gaussian multinomial coefficients as the generating function for certain restricted paths.

UR - https://www.scopus.com/pages/publications/49049140626

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M3 - Article

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JF - Journal of Combinatorial Theory, Series A

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q-Counting n-dimensional lattice paths

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