In this project we will investigate a family of polytopes called graph associahedra. In particular we will investigate the conjecture by D’León-Wachs about the relation between the graph associahedra constructed from trees and the weighted partition posets. This conjecture states that the face-vector of the graph associahedra is related to the homology of the weighted partition posets. This conjecture has been verified for trees with up to 9 vertices. We will use open-source software to further investigate this problem.
Completion of Calculus 3. Familiarity with python is ideal.