What persistent data structure for a set of partially ordered elements?
The paper "Sorting and Selection in PoSets" by Daskalakis, Karp, Mossel, Risensefield, Verbin, 2008 which describes a dynamic representation of PoSets based on antichains.

You might also be interested in the paper "Succinct Posets" by Munro, Nicholson, 2012 recently released on Arxiv and in the bibliography therein. Their data-structure is static but I assume that the next step is to have a dynamical data-structure.