A partial order structure on interval orders
  We introduce a partial order structure on the set of interval orders of a given size, and prove that such a structure is in fact a lattice. We also provide a way to compute meet and join inside this lattice. Finally, we show that, if we restrict to series parallel interval order, what we obtain is the classical Tamari poset. 
Filippo Disanto, Luca Ferrari and Simone Rinaldi
math.CO cs.DM