Part of the graph [G, o]. The upper half, excluding the vertices on the axis of symmetry, is G 0 . If v a := (a, 0), then the vertices of G 0 shown in this figure are v −3 , v −2 , v −1 , v −1/2 , v 0 , v 1/4 , v 1/2 , v 3/4 , v 1 , v 3 , v 5 from left to right. One has p(v −2 ) = p(v 0 ) = v −1 , p(v −1 ) = p(v 3 ) = 1, p(v −1/2 ) = p(v 1/2 ) = 0 and p(v 1/4 ) = p(v 3/4 ) = 1/2. Also, v 1 ∈ L −2 , {v −1 , v 3 } ⊆ L −1 , {v −2 , v 0 } ⊆ L 0 , {v −1/2 , v 1/2 } ⊆ L 1 and {v 1/4 , v 3/4 } ⊆ L 2 .

Contexts in source publication

Context 1

... a graph G 0 is constructed in the upper half plane such that its faces are triangles and all edges are semicircles (see Figure 3). In this graph, each triangle is of the form t a,b , where t a,b is the triangle with vertex set ...

Context 2

... the genealogical structure of the triangles induces a similar structure on the vertices. For each vertex v, let p(v) denote its parent (see Figure 3). Let l(v, w) denote the number of generations between v and w, which is defined by the equations l(v, v) := 0 and l(v, p(v)) = −1. ...

Context 3

... a graph G 0 is constructed in the upper half plane such that its faces are triangles and all edges are semicircles (see Figure 3). In this graph, each triangle is of the form t a,b , where t a,b is the triangle with vertex set ...

Context 4

... the genealogical structure of the triangles induces a similar structure on the vertices. For each vertex v, let p(v) denote its parent (see Figure 3). Let l(v, w) denote the number of generations between v and w, which is defined by the equations l(v, v) := 0 and l(v, p(v)) = −1. ...