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The Number of Four Dimensional PL-spheres with Nine Vertices
| DC Field | Value | Language |
|---|---|---|
| dc.contributor.advisor | 최수영 | - |
| dc.contributor.author | 장현태 | - |
| dc.date.accessioned | 2022-11-29T02:32:19Z | - |
| dc.date.available | 2022-11-29T02:32:19Z | - |
| dc.date.issued | 2020-08 | - |
| dc.identifier.other | 30337 | - |
| dc.identifier.uri | https://dspace.ajou.ac.kr/handle/2018.oak/19834 | - |
| dc.description | 학위논문(석사)--아주대학교 일반대학원 :수학과,2020. 8 | - |
| dc.description.tableofcontents | 1. Introduction 1 2. PL-spheres 2 2.1 SImple and Simplicial Polytopes 2 2.2 PL-Spheres 4 3. Real Toric Spaces 8 3.1 Real Toric Spaces 8 3.2 Dual Characteristic Maps 12 4. Enumeration of PL-Spheres 16 4.1 Bistellar Moves 16 4.2 Lexicographic Enumeration 18 References 24 Appendix A Gale Diagrams 27 | - |
| dc.language.iso | eng | - |
| dc.publisher | The Graduate School, Ajou University | - |
| dc.rights | 아주대학교 논문은 저작권에 의해 보호받습니다. | - |
| dc.title | The Number of Four Dimensional PL-spheres with Nine Vertices | - |
| dc.type | Thesis | - |
| dc.contributor.affiliation | 아주대학교 일반대학원 | - |
| dc.contributor.department | 일반대학원 수학과 | - |
| dc.date.awarded | 2020. 8 | - |
| dc.description.degree | Master | - |
| dc.identifier.localId | 1151748 | - |
| dc.identifier.uci | I804:41038-000000030337 | - |
| dc.identifier.url | http://dcoll.ajou.ac.kr:9080/dcollection/common/orgView/000000030337 | - |
| dc.subject.keyword | PL-sphere | - |
| dc.subject.keyword | bistellar move | - |
| dc.subject.keyword | lexicographic enumeration | - |
| dc.subject.keyword | real toric space | - |
| dc.subject.keyword | toric topology | - |
| dc.description.alternativeAbstract | We study the number of D-J classes on P L-spheres with a few vertices. The Picard number of a P L-sphere with m vertices of dimension n − 1 is defined as m − n. It is known that all PL-spheres with Picard numbers less than 4 are polytopal, and the number is well-known by Perles. Furthermore, the numbers of D-J classes over such PL-spheres have been computed by Choi and Park. Nevertheless, only little is known about P L-spheres with the Picard number 4. In this thesis, we focus on PL-spheres of the Picard number 4. It is known that there are 5 PL-spheres of dimension 2 as a corollary of Steinitz’s theorem, and 39 of dimension 3 by Barnette. We construct two algorithms to count 4 dimensional P L-spheres of the Picard number 4; one gives the lower bound and the other gives the upper bound. Using this, we show that there are exactly 337 P L-spheres of dimension 4 with 9 vertices. As a corollary, we show that there are exactly 15757 D-J classes over such PL-spheres. | - |
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- Graduate School of Ajou University > Department of Mathematics > 3. Theses(Master)
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