Exploiting symmetry on the Universal Polytope
| العنوان: | Exploiting symmetry on the Universal Polytope |
|---|---|
| المؤلفون: | Pfeifle, Julián |
| المساهمون: | Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada II, Universitat Politècnica de Catalunya. MD - Matemàtica Discreta |
| المصدر: | Recercat. Dipósit de la Recerca de Catalunya instname UPCommons. Portal del coneixement obert de la UPC Universitat Politècnica de Catalunya (UPC) |
| مصطلحات موضوعية: | 52B Polytopes and polyhedra, Polytopes, Discrete geometry, Matemàtiques i estadística::Geometria::Geometria convexa i discreta [Àrees temàtiques de la UPC], Geometria discreta, Politops, 52C Geometria discreta |
| الوصف: | The most successful method to date for finding lower bounds on the number of simplices needed to triangulate a given polytope P involves optimizing a linear functional over the associated Universal Polytope U(P). However, as the dimension of P grows, these linear programs become increasingly difficult to formulate and solve. Here we present a method to algorithmically construct the quotient of U(P) by the symmetry group Aut(P) of P, which leads to dramatic reductions in the size of the linear program. We compare the power of our approach with older computations by Orden and Santos, indicate the influence of the combinatorial complexity barrier on these computations, and sketch some future applications. |
| وصف الملف: | application/pdf |
| URL الوصول: | https://explore.openaire.eu/search/publication?articleId=dedup_wf_001::4330c75e17b92b2c48b4b54a66811e5c http://hdl.handle.net/2117/17663 |
| Rights: | OPEN |
| رقم الانضمام: | edsair.dedup.wf.001..4330c75e17b92b2c48b4b54a66811e5c |
| قاعدة البيانات: | OpenAIRE |
| الوصف غير متاح. |