English

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.

Keywords

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

R2 v1 2026-06-21T11:14:05.963Z