On partitions avoiding 3-crossings

Mireille Bousquet-Mélou, Guoce Xin

A partition on $[n]$ has a crossing if there exists $i\_1<i\_2<j\_1<j\_2$ such that $i\_1$ and $j\_1$ are in the same block, $i\_2$ and $j\_2$ are in the same block, but $i\_1$ and…