Riordan matrices and higher-dimensional lattice walks |
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Authors: | Asamoah Nkwanta |
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Institution: | Department of Mathematics, Morgan State University, Baltimore, MD 21251, USA |
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Abstract: | An algebraic combinatorial method is used to count higher-dimensional lattice walks in Zm that are of length n ending at height k. As a consequence of using the method, Sands’ two-dimensional lattice walk counting problem is generalized to higher dimensions. In addition to Sands’ problem, another subclass of higher-dimensional lattice walks is also counted. Catalan type solutions are obtained and the first moments of the walks are computed. The first moments are then used to compute the average heights of the walks. Asymptotic estimates are also given. |
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Keywords: | Riordan array Riordan matrix Higher-dimensional lattice walks First moments |
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