Face enumeration of convex polytopes and cell complexes
Project/Area Number |
25400043
|
Research Category |
Grant-in-Aid for Scientific Research (C)
|
Allocation Type | Multi-year Fund |
Section | 一般 |
Research Field |
Algebra
|
Research Institution | Osaka University (2014-2015) Yamaguchi University (2013) |
Principal Investigator |
Murai Satoshi 大阪大学, 情報科学研究科, 准教授 (90570804)
|
Project Period (FY) |
2013-04-01 – 2016-03-31
|
Project Status |
Completed (Fiscal Year 2015)
|
Budget Amount *help |
¥5,070,000 (Direct Cost: ¥3,900,000、Indirect Cost: ¥1,170,000)
Fiscal Year 2015: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
Fiscal Year 2014: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
Fiscal Year 2013: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
|
Keywords | 凸多面体 / cd指数 / 三角形分割 / スタンレー・ライスナー環 / f列 / 次数付ベッチ数 / cd index / f-列 |
Outline of Final Research Achievements |
In this research project, we study the face numbers of polytopes and cell complexes. The followings are main results of this project. (1) We find new method to study the cd-index of a convex polytope by using commutative algebra, and by applying this new method, we find new upper bounds of the cd-index. (2) We find new applications of polyhedral Morse inequality and graded Betti numbers to the study of face numbers of triangulated manifolds.
|
Report
(4 results)
Research Products
(19 results)