I will define a poset relation on the symmetric group Sn, which gives a natural order-preserving function from Sn to the lattice of partitions. If we restrict our attention to elements in Sn under a particular n-cycle, we have a lattice which is isomorphic to the lattice of non-crossing partitions. If time permits I'll talk about some of the implications.
This work is based on a paper by Thomas Brady.