Study of enumerations of plane partitions and evaluations of determinants and Pfaffians from the aspect of hypergeometric series

在这项科研资助下，我们取得了丰硕的研究成果。首先，我们的论文《次要求和公式和Stanley’s open problem的一个证明》在2007年意大利西西里岛陶尔米纳举行的第17届国际形式幂级数与代数组合会议上被接受作报告。2005年6月20日至25日。我们的论文“The Andrews-Stanley配分函数和Al-Salam-Chihara多项式”也被2006年6月19-23日在美国加州圣地亚哥举行的第18届国际形式幂级数与代数组合会议作为海报接受。我们还参加了每半年在欧洲举行的Lotharingien de Combinatoire研讨会，并与来自世界各国的许多外国研究人员就代数组合学及相关领域的几个主题进行了交流和讨论。2005年，我们支持法国克劳德伯纳德大学卡米尔乔丹研究所曾江教授访问日本三周。我们对Andrews-Stanley配分函数和Al-Salam-Chihara多项式进行了大量的讨论，并一起参加了在京都举行的“组合表示理论的世界”和在静冈举行的“表示理论研讨会”。我们还拜访了东京大学的寺田itaru教授，江曾教授在东京大学做了演讲。我和姜增教授在京都的会议上各作了一次报告。我也有机会在参加会议的场合多次访问卡米尔·乔丹研究所，克劳德·伯纳德·里昂大学1，在组合和理论的组合中做正交多项式和平面分割的演讲。我们还与Frederic joheet和Anisse Kasraoui讨论了Hall-Littlewood多项式和Roger-Ramanujan型恒等式，或集的有序划分和q-Stirling数的统计。我们也在完全对称自互补平面分区的精炼枚举的mills - robbins - rumsey猜想上取得了进展。这些猜想已经公开了二十多年，并引起了许多与交替符号矩阵研究相关的研究者的兴趣。最后，我们对soich Okada教授和Alain Lascoux教授提出的宝贵意见和建议深表感谢。少

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 … More 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