Crossings and Nestings of Two Edges in Set Partitions

Svetlana Poznanovik, Catherine Yan

Let $\pi$ and $\lambda$ be two set partitions with the same number of blocks. Assume $\pi$ is a partition of $[n]$. For any integer $l,m\ge 0$, let $\mathcal{T}(\pi ,l)$ be the set of parti…