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

作者：Upperman Johnathon; Vinroot C Ryan^*

来源：Discrete Mathematics, 2014, 315: 9-17.

DOI：10.1016/j.disc.2013.10.002

• Symmetric group
• m-cycles
• Bruhat order
• EL-shellable posets

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 m-cycles in the symmetric group, and we generalize all of the results of Deodhar and Srinivasan just mentioned to the case of any m %26gt;= 2.

• 出版日期2014-2-6