Reduced expressions for the elements in a Bruhat interval

Let (W, S) be a Coxeter system. We study the relation among the reduced expressions of the elements in the interval [y, w] := {z is an element of W vertical bar y <= z <= w} for any y < w in W. Fix a reduced expression xi of w. We find some conditions for various expressions zeta to be reduced, where zeta is obtained from xi by deleting certain factors in S. We investigate the relations among all such which are reduced expressions for either a certain element in [y, w] or some elements with a certain common property. (C) 2019 Elsevier B.V. All rights reserved.