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Displaying similar documents to “Commensurability of graph products.”

Structure of geodesics in the Cayley graph of infinite Coxeter groups

Ryszard Szwarc (2003)

Colloquium Mathematicae

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Let (W,S) be a Coxeter system such that no two generators in S commute. Assume that the Cayley graph of (W,S) does not contain adjacent hexagons. Then for any two vertices x and y in the Cayley graph of W and any number k ≤ d = dist(x,y) there are at most two vertices z such that dist(x,z) = k and dist(z,y) = d - k. Allowing adjacent hexagons, but assuming that no three hexagons can be adjacent to each other, we show that the number of such intermediate vertices at a given distance from...