Non-Crossing Tableaux
  In combinatorics there is a well-known duality between non-nesting and non-crossing objects. In algebra there are many objects which are standard, for example Standard Young Tableaux, Standard Monomials, Standard Bitableaux. We adopt a point of view that these standard objects are really non-nesting, and we find their non-crossing counterparts. 
Pavlo Pylyavskyy