Circular Digraph Walks, k-Balanced Strings, Lattice Paths and Chebychev Polynomials
Combinatorics
2008-08-28 v1
Abstract
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.
Cite
@article{arxiv.0808.3614,
title = {Circular Digraph Walks, k-Balanced Strings, Lattice Paths and Chebychev Polynomials},
author = {Evangelos Georgiadis and David Callan and Qing-Hu Hou},
journal= {arXiv preprint arXiv:0808.3614},
year = {2008}
}
Comments
12 pages, 1 figure, 2 tables. Submitted.Accepted