Crossings and nestings of two edges in set partitions

Combinatorics Seminar
Friday, September 24, 2010 - 15:05
1 hour (actually 50 minutes)
Skiles 255
SoM, Georgia Tech
A set partition of [n] can be represented graphically by drawing n dots on a horizontal line and connecting the points in a same block by arcs. Crossings and nestings are then pairs of arcs that cross or nest. Let G be an abelian group, and \alpha, \beta \in G. In this talk I will look at the distribution of the statistic s_{\alpha, \beta} = \alpha * cr + \beta * ne on subtrees of the tree of all set partitions and present a result which says that the distribution of s_{\alpha, \beta} on a subtree is determined by its distribution on the first two levels.