| Project/Area Number |
25400018
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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 | University of the Ryukyus |
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Principal Investigator |
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| Co-Investigator(Kenkyū-buntansha) |
OKADA Soichi 名古屋大学, 多元数理科学研究科, 教授 (20224016)
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| Co-Investigator(Renkei-kenkyūsha) |
TAGAWA Hiroyuki 和歌山大学, 教育学部, 教授 (80283943)
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| Project Period (FY) |
2013-04-01 – 2016-03-31
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| Project Status |
Completed (Fiscal Year 2015)
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| Budget Amount *help |
¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000)
Fiscal Year 2015: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2014: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2013: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000)
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| Keywords | 数え上げ組合せ論 / 表現論 / 数理物理 / タイリング / 代数的組合せ論 / ダイマーモデル / 対称関数 / 直交多項式 / タイリング問題 / 超幾何級数 / パフィアン / 行列式 / 平面分割の数え上げ / 母関数 / d-complete posets / Macdonald polynomials |
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| Outline of Final Research Achievements |
We studied Pfaffian analogue of q-Catalan Hankel determinant and the Askey-Habsieger-Kadell q-Selberg's integral formula using de Bruijn's formula. We also obtained similar results for certain q-Pfaffian whose entries are moments of Al-Salam-Carlitz polynomials using a result by Baker and Forrester. We also studied a q-analogue of Mehta-Wang determinant and reduced it to a quadratic equation for the Askey-Wilson polynomials, which was a joint-work with V. Guo, H. Tagawa and J. Zeng. We also studied a combinatorial proof of a couple of Pfaffian identities with T. Eisenkoelbl and J. Kim. Recently I had some results on the enumeration of domino tilings of Aztec rectangle with holes. The enumeration problems are closely related to the combinatorial methods, e.g. the Gessel-Viennot Lattice path method, Kasteleyn's method and the enumeration of spanning trees of graph. In this research we obtain a determinant expression for the enumeration appealing to the Gessel-Viennot method.
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