doi:10.1112/blms/bdr134 Reflection length in non-affine Coxeter groups

Duszenko The reflection length of an element of a Coxeter group is the minimal number of conjugates of the standard generators whose product is equal to that element. In this paper, we prove the conjecture of McCammond and Petersen that reflection length is unbounded in any non-affine Coxeter group. Among the tools used, the construction of word-hyperbolic quotients of all minimal non-affine Coxeter groups might be of independent interest. 1