Physical Sciences and Mathematics Commons^™

Flag F-Vectors Of Polytopes With Few Vertices, Sarah A. Nelson

Theses and Dissertations--Mathematics

We may describe a polytope P as the convex hull of n points in space. Here we consider the numbers of chains of faces of P. The toric g-vector and CD-index of P are useful invariants for encoding this information. For a simplicial polytope P, Lee defined the winding number w_k in a Gale diagram corresponding to P. He showed that w_k in the Gale diagram equals g_k of the corresponding polytope. In this dissertation, we fully establish how to compute the g-vector for any polytope with few vertices from its …