2012 Fiscal Year Final Research Report
Statistical analysis of rankings and hyperplane arrangements
| Project/Area Number |
22540134
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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 | Nagoya University (2011-2012)
Okayama University (2010) |
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Principal Investigator |
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| Project Period (FY) |
2010 – 2012
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| Keywords | 統計数学 |
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| Research Abstract |
In the general setting of the theory of hyperplane arrangements, we studied properties of a hyperplane arrangement which is stable under the action of a Coxeter group and obtained some results such as the number of the orbits of the chambers of this arrangement. Moreover, applying the general results to the problem of rankings, we found the exact number of essentially different ranking patterns which can be generated by the unfolding model of codimension one. Applying the general results to another problem, we also investigated properties of a preference order called semiorder. Besides, we defined a family of distributions and examined its properties in the general setting of group invariance.
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