| Project/Area Number |
26400086
|
|---|
| Research Category |
Grant-in-Aid for Scientific Research (C)
|
| Allocation Type | Multi-year Fund |
|---|
| Section | 一般 |
|---|
| Research Field |
Geometry
|
|---|
| Research Institution | University of the Ryukyus (2016)
Kyoto University (2014-2015) |
|---|
Principal Investigator |
|
|---|
| Co-Investigator(Kenkyū-buntansha) |
上 正明 京都大学, 理学研究科, 教授 (80134443)
|
|---|
| Co-Investigator(Renkei-kenkyūsha) |
SATOH Takao 東京理科大学, 第二理学部, 講師 (70533256)
KAWAZUMI Nariya 東京大学, 大学院数理科学研究科, 准教授 (30214646)
SAITO Kyoji 東京大学, 数物連携宇宙研究機構, 主任研究員 (20012445)
|
|---|
| Project Period (FY) |
2014-04-01 – 2017-03-31
|
| Project Status |
Completed (Fiscal Year 2016)
|
| Budget Amount *help |
¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000)
Fiscal Year 2016: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2015: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2014: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
|
|---|
| Keywords | 増大級数 / 有限生成群 / 有理関数表示 / トーラス結び目群 / ケーリー・グラフ / オートマトン / ザイフェルト束 / 測地的代表元 / アルティン群 / 融合積 / 二面体群 |
|---|
| Outline of Final Research Achievements |
The head investigator Fujii obtained several results concerning the growth series for a group G(p,q),
which is determined if arbitrary integers greater than or equal to two, p and q, are given.
First, Fujii described a necessary and sufficient condition for a representative of an element g of G(p,q) to be shortest among all representatives of g. Next, Fujii gave a rational function expression for the spherical growth series for G(p,q). Moreover, Fujii constructed a finite state automaton which accepts all of the shortest representatives of G(p,q), and obtained a rational function expression for the geodesic growth series for G(p,q).
|
