Restricted Walks in Regular Trees

Laura Ciobanu, Saša Radomirović

Abstract


Let ${\cal T}$ be the Cayley graph of a finitely generated free group $F$. Given two vertices in ${\cal T}$ consider all the walks of a given length between these vertices that at a certain time must follow a number of predetermined steps. We give formulas for the number of such walks by expressing the problem in terms of equations in $F$ and solving the corresponding equations.


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