Probabilistic and pseudo-probabilistic methods in combinatorics and their applications
| Project/Area Number |
19540119
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
General mathematics (including Probability theory/Statistical mathematics)
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| Research Institution | The University of Electro-Communications |
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Principal Investigator |
ISHIGAMI Yoshiyasu The University of Electro-Communications, 大学院・情報理工学研究科, 准教授 (50262374)
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| Project Period (FY) |
2007 – 2010
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| Project Status |
Completed (Fiscal Year 2010)
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| Budget Amount *help |
¥4,550,000 (Direct Cost: ¥3,500,000、Indirect Cost: ¥1,050,000)
Fiscal Year 2010: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2009: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2008: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2007: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
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| Keywords | 組合せ論 / ラムゼー理論 / 超グラフ / 擬ランダム |
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| Research Abstract |
A theorem in graph theory called Szemeredi's regularity lemma is known to be useful in many combinatorial problems including additive number theory and others. This theorem has been expanded in a simple form. In previously known versions of this theorem, the constructions of the desired decompositions was obtained by repeating a complicated process. In this version, the desired decomposition is obtained almost surely by a one-time simple random sampling. By utilizing this advantage, this theorem is applied to several problems and its power is demonstrated.
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Report
(6 results)
Research Products
(14 results)
