Date of Award
Doctor of Philosophy (PhD)
Richard M. Green
We present a complete acyclic matching of the Hasse diagram associated with the face lattice of a hypersimplex. Since a hypersimplex is a convex polytope, there is a natural way to form a CW complex from its faces. We will then utilize this matching along with discrete Morse theory and some topological techniques to classify every subcomplex whose reduced homology groups are concentrated in a single degree. These reduced homology groups support a natural action of the symmetric group and a description of the characters that this action produces is given.
Harper, Jacob Tyler, "Homology Representations Arising from a Hypersimplex" (2011). Mathematics Graduate Theses & Dissertations. 9.