2015 Fiscal Year Final Research Report
Research on combinatorics with representation theory related to leaf posets and surrounding topics
| Project/Area Number |
23540017
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Algebra
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| Research Institution | Wakayama University |
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Principal Investigator |
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| Project Period (FY) |
2011-04-28 – 2016-03-31
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| Keywords | hook length poset / d-complete poset / leaf poset / 行列式 / 超幾何級数 / Askey-Wilson 多項式 / Aztec rectangle |
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| Outline of Final Research Achievements |
In this research, we mainly obtained the following results: We found that the d-complete poset being multivariable hook length poset implies the leaf poset being multivariable hook length poset. We expressed the number of the domino tilings in the Aztec rectangle with connected 2r-holes by a determinant of the matrix of size 2r whose elements are hypergeometric series. We proved a quadratic formula of hypergeometirc series which is useful for the proof of some kind of Hankel type determinants.
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| Free Research Field |
代数的組合せ論
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