Circular Digraph Walks, k-Balanced Strings, Lattice Paths and Chebychev Polynomials

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We count the number of walks of length n on a k-node circular digraph that cover all k nodes in two ways. The first way illustrates the transfer-matrix method. The second involves counting various classes of height-restricted lattice paths. We observe that the results also count so-called k-balanced strings of length n, generalizing a 1996 Putnam problem.
12 pages, 1 figure, 2 tables. Submitted.Accepted

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Combinatorics, 05A05; 05A15

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http://salesiana.dossiersoluciones.com/handle/123456789/167794

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/0808.3614
 http://arxiv.org/abs/0808.3614
 The Electronic Journal of Combinatorics 15 (2008), #R108

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arXiv