Coxeter groups The conjugacy problem The Root automaton References

A Coxeter system consists of a group W (called a Coxeter group) generated by a set S of involutions with presentation W = hS j s2 = 1; (st)m(s;t) = 1i where m(s; t) 2 for s 6 = t. Since s and t are involutions, the relation (st)m(s;t) = 1 can be rewritten as m(s; t) = 2 =) st = ts short braid relations m(s; t) = 3 =) sts = tst m(s; t) = 4 =) stst = tst