On the number of walks on a regular Cayley tree

Details On the number of walks on a regular Cayley tree On the number of walks on a regular Cayley tree

2009-03-10

arxiv.org/abs/0903.1877v2

Mathematics

Combinatorics

4 pages; added references to literature

Scientific paper

We provide a new derivation of the well-known generating function counting the number of walks on a regular tree that start and end at the same vertex, and more generally, a generating function for the number of walks that end at a vertex a distance i from the start vertex. These formulas seem to be very old, and go back, in an equivalent form, at least to Harry Kesten's work on symmetric random walks on groups from 1959, and in the present form to Brendan McKay (1983).

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