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

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

2008-08-27

arxiv.org/abs/0808.3614v1

The Electronic Journal of Combinatorics 15 (2008), #R108

Mathematics

Combinatorics

12 pages, 1 figure, 2 tables. Submitted.Accepted

Scientific paper

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.

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