Restricted walks

Let T be an innite regular tree and n a positive integer. Fix two vertices x and y in T . By a walk or a path between x and y we mean any nite sequence of edges that connect x and y in which backtrackings are allowed. There are many formulas in the literature which give the number of walks of length n between x and y, such as recurrence formulas, generating functions, Green functions, and others. Here we consider walks of length n between x and y which at a certain time follow a number of predetermined steps....

18p thulanh6 14-09-2011 37 5   Download