Complexes of trees and nested set complexes
Eva María Feichtner · Pacific Journal of Mathematics · 2006
We exhibit an identity of abstract simplicial complexes between the wellstudied complex of trees T n and the reduced minimal nested set complex of the partition lattice.We conclude that the order complex of the partition lattice can be obtained from the complex of trees by a sequence of stellar subdivisions.We provide an explicit cohomology basis for the complex of trees that emerges naturally from this context.Motivated by these results, we review the generalization of complexes of trees to complexes of k-trees by Hanlon, and we propose yet another generalization, more natural in the context of nested set complexes.