GENERAL FLIPS AND THE CD-INDEX

GENERAL FLIPS AND THE CD-INDEX

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 re...

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Bibliographic Details
Main Author: Wells, Daniel J.
Format: Others
Published: UKnowledge 2010
Subjects:
combinatorial geometry
polytopes
bistellar flips
cd-index
PL-spheres
Mathematics
Online Access:http://uknowledge.uky.edu/gradschool_diss/33
http://uknowledge.uky.edu/cgi/viewcontent.cgi?article=1032&context=gradschool_diss
id ndltd-uky.edu-oai-uknowledge.uky.edu-gradschool_diss-1032
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spelling ndltd-uky.edu-oai-uknowledge.uky.edu-gradschool_diss-10322015-04-11T05:00:49Z GENERAL FLIPS AND THE CD-INDEX Wells, Daniel J. 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. 2010-01-01T08:00:00Z text application/pdf http://uknowledge.uky.edu/gradschool_diss/33 http://uknowledge.uky.edu/cgi/viewcontent.cgi?article=1032&context=gradschool_diss University of Kentucky Doctoral Dissertations UKnowledge combinatorial geometry polytopes bistellar flips cd-index PL-spheres Mathematics
collection NDLTD
format Others
sources NDLTD
topic combinatorial geometry
polytopes
bistellar flips
cd-index
PL-spheres
Mathematics
spellingShingle combinatorial geometry
polytopes
bistellar flips
cd-index
PL-spheres
Mathematics
Wells, Daniel J.
GENERAL FLIPS AND THE CD-INDEX
description 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.
author Wells, Daniel J.
author_facet Wells, Daniel J.
author_sort Wells, Daniel J.
title GENERAL FLIPS AND THE CD-INDEX
title_short GENERAL FLIPS AND THE CD-INDEX
title_full GENERAL FLIPS AND THE CD-INDEX
title_fullStr GENERAL FLIPS AND THE CD-INDEX
title_full_unstemmed GENERAL FLIPS AND THE CD-INDEX
title_sort general flips and the cd-index
publisher UKnowledge
publishDate 2010
url http://uknowledge.uky.edu/gradschool_diss/33
http://uknowledge.uky.edu/cgi/viewcontent.cgi?article=1032&context=gradschool_diss
work_keys_str_mv AT wellsdanielj generalflipsandthecdindex
_version_ 1716800460267978752

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