A weight statistic and partial order on products of mm-cycles

R. S. Deodhar and M. K. Srinivasan defined a weight statistic on the set of involutions in the symmetric group and proved several results about the properties of this weight. These results include a recursion for a weight generating function, that the weight provides a grading for the set of fixed-point free involutions under a partial order related to the Bruhat partial order, and that this graded poset is EL-shellable and its order complex triangulates a ball. We extend the definition of weight to products of disjoint mm-cycles in the symmetric group, and we generalize all of the results of Deodhar and Srinivasan just mentioned to the case of any m≥2m≥2.