A Bijection for Crossings and Nestings
  For a subclass of matchings, set partitions, and permutations, we describe a direct bijection involving only arc annotated diagrams that not only interchanges maximum nesting and crossing numbers, but also all refinements of crossing and nesting numbers. Furthermore, we show that the bijection cannot be applied to a similar class of coloured arc annotated diagrams. 
Lily Yen
math.CO