A generating tree approach to k-nonnesting partitions and permutations
  We describe a generating tree approach to the enumeration and exhaustive generation of k-nonnesting set partitions and permutations. Unlike previous work in the literature using the connections of these objects to Young tableaux and restricted lattice walks, our approach deals directly with partition and permutation diagrams. We provide explicit functional equations for the generating functions, with k as a parameter. 
Sophie Burrill, Sergi Elizalde, Marni Mishna, Lily Yen
math.CO