  We introduce a new combinatorial object called tower diagrams and prove
fundamental properties of these objects. We also introduce an algorithm that
allows us to slide words to tower diagrams. We show that the algorithm is
well-defined only for reduced words which makes the algorithm a test for
reducibility. Using the algorithm, a bijection between tower diagrams and
finite permutations is obtained and it is shown that this bijection specializes
to a bijection between certain labellings of a given tower diagram and reduced
expressions of the corresponding permutation.
