On minimal lengths of expressions of Coxeter group elements as products ofreflections

It is shown that the absolute length iota'(w) of a Coxeter group element w (i.e. the minimal length of an expression of w as a product of reflections) is equal to the minimal number of simple reflections that must be deleted from a fixed reduced expression of w so that the resulting product is equal to e, the identity element. Also, iota'(w) is the minimal length of a path in the (directed) Bruhat graph from the identity element e to w, and iota' (w) is determined by the polynomial R-e,R-w of Kazhdan and Lusztig.