Involution products in Coxeter groups

For W a Coxeter group, let = {w ∈ W | w = xy where x, y ∈ W and x2 = 1 = y2}. It is well known that if W is finite then W = . Suppose that w ∈ . Then the minimum value of ℓ(x) + ℓ(y) - ℓ(w), where x, y ∈ W with w = xy and x2 = 1 = y2, is called the excess of w (ℓ is the length function of W). The main result established here is that w is always W-conjugate to an element with excess equal to zero. © 2011 de Gruyter.