Abstract
A cube complex is a regular cell complex X all of whose cells are cubes and such that the intersection of any two cells is a face of both. An edge-path in a cube complex X is a sequence e1; : : : ; en of oriented edges such that the head of ei coincides with the tail of eiC1 for 1 i n 1. The number of edges in an edge-path is called the length of the path. Given two vertices x;x in a cube complex X , we define the distance d.x;x/ to be the minimum length (possibly infinite) of an edge-path connecting x to x . For each vertex x0 in X , we let G.X;x0I t/ denote the corresponding growth series for X . That is,
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