Date Available
4-8-2011
Year of Publication
2010
Degree Name
Doctor of Philosophy (PhD)
Document Type
Dissertation
College
Arts and Sciences
Department
Mathematics
First Advisor
Dr. Carl W Lee
Abstract
We generalize bistellar operations (often called flips) on simplicial manifolds to a notion of general flips on PL-spheres. We provide methods for computing the cd-index of these general flips, which is the change in the cd-index of any sphere to which the flip is applied. We provide formulas and relations among flips in certain classes, paying special attention to the classic case of bistellar flips. We also consider questions of "flip-connecticity", that is, we show that any two polytopes in certain classes can be connected via a sequence of flips in an appropriate class.
Recommended Citation
Wells, Daniel J., "GENERAL FLIPS AND THE CD-INDEX" (2010). University of Kentucky Doctoral Dissertations. 33.
https://uknowledge.uky.edu/gradschool_diss/33
