Date of Award

Spring 1-1-2011

Document Type


Degree Name

Doctor of Philosophy (PhD)



First Advisor

Richard M. Green

Second Advisor

Nathaniel Thiem

Third Advisor

Marty Walter


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.

Included in

Mathematics Commons