Liu, GakuMason, Alexander Charles2024-09-092024-09-092024Mason_washington_0250E_26764.pdfhttps://hdl.handle.net/1773/52105Thesis (Ph.D.)--University of Washington, 2024We study the behavior of $h$-vectors associated to matroid complexes under weak maps, or inclusions of matroid polytopes. Specifically, we show that the $h$-vector of the order complex of the lattice of flats of a matroid is component-wise non-increasing under a weak map. This result extends to the flag $h$-vector. We note that the analogous result also holds for independence complexes and rank-preserving weak maps.application/pdfen-USCC BYalgebraic combinatoricscombinatoricsmatroidssimplicial complexesMathematicsMathematicsThesis