Study of enumerations of plane partitions and evaluations of determinants and Pfaffians from the aspect of hypergeometric series
| Project/Area Number |
17540024
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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 |
Algebra
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| Research Institution | Tottori University |
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Principal Investigator |
ISHIKAWA Masao Tottori University, University Education Center, Associate Professor, 大学教育総合センター, 助教授 (40243373)
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| Project Period (FY) |
2005 – 2006
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| Project Status |
Completed (Fiscal Year 2006)
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| Budget Amount *help |
¥2,400,000 (Direct Cost: ¥2,400,000)
Fiscal Year 2006: ¥1,000,000 (Direct Cost: ¥1,000,000)
Fiscal Year 2005: ¥1,400,000 (Direct Cost: ¥1,400,000)
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| Keywords | Determinants / Pfaffians / Algebraic combinatorics / Symmetric polynomials / Representation theory / Plane partitions / Symmetric groups / Hypergemetric series / 平面分割 / 超幾何級数 / Pfaffian / hook length formula / d-complete poset / hypergeometric series / symmetry / generating functions / determinant |
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| Research Abstract |
We had fruitful research results with this Grant-in-Aid for scientific research. First of all, our paper "Minor summation formula and a proof of Stanley's open problem" was accepted for a talk in the 17^<th> International Conference on Formal Power Series and Algebraic Combinatorics held in Taormina, Sicily, Italy during. June 20-25, 2005. Our paper "The Andrews-Stanley Partition Function and Al-Salam-Chihara Polynomials" was also accepted for a poster in the 18^<th> International Conference on Formal Power Series and Algebraic Combinatorics held in San Diego California, United States of America during June 19-23, 2006. We also joined the Seminaire Lotharingien de Combinatoire held every half year in Europe, and exchanged information and discussed on the several subjects of the algebraic combinatorics and related area with many foreign researchers from various h countries in the world. In 2005, we supported Professor Jiang Zeng from Institut Camille Jordan, Universite Claude Bernard Ly
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on 1 visiting Japan for three weeks. We discussed a lot on the Andrews-Stanley partition function and Al-Salam-Chihara polynomials and travel together to participate in the conferences The World of Combinatorial Representation Theory held in Kyoto and The Symposium on Representation Theory held in Shizuoka. We also visited Prof.Itaru Terada in University of Tokyo and Prof.Jiang Zeng gave a talk in the University. Each of I and Prof.Jiang Zeng gave a talk in the confence in Kyoto. I also had chances to visit Institut Camille Jordan, Universite Claude Bernard Lyon 1 several times in the occasions of attending the conferences Seminaire Lotharingien de Combinatoire, gave talks on orthogonal polynomials and plane partitions at Combinatoire et Theorie des Nombres. We also had discussions with Frederic Johet and Anisse Kasraoui on the Hall-Littlewood polynomials and Roger-Ramanujan type identities, or Statistics on Ordered Partitions of Sets and q-Stirling Numbers. We also had progresses on the Mills-Robins-Rumsey conjectures of the refined enumerations of totally symmetric self-complementary plane partitions. These conjectures have been open more than twenty years and attracted the interests of many researched related to the study of the alternating sign matrices. Lastly we would like to express our deep appreciation Prof.Soich Okada and Alain Lascoux for their valuable comments and suggestions. Less
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Report
(3 results)
Research Products
(13 results)
