This talk will be about finite lattices and posets.  I’ll tell you what an EL-labeling is, explain how the subgroup lattice of a supersolvable group motivates its definition, and give related results on lattices defined from groups. Unfortunately, EL-labelings can be difficult to construct, and there are several lattices for which it is not known whether an EL-labeling exists.  I’ll show how this leads to the idea of a CL-labeling.

My goal, if time allows, is to give a clear idea of recent work of myself and Jay Schweig, in which we show that a certain wide class of lattices has a CL-labeling.