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

我们在这项科研资助计划下取得了丰硕的研究成果。首先，我们的论文“Minor summation formula and a proof of Stanley's open problem”在<th>年于意大利西西里的陶尔米纳举行的第17届国际形式幂级数和代数组合学会议上被录用为报告。2005年6月20日至25日。2006年6月19日至23日，在美国加州圣地亚哥举行的第18届国际形式幂级数和代数组合学会议上，我们的论文“Andrews-Stanley Partition Function and Al-Salam-Chihara Polynomials”也被接受为海报<th>。我们还参加了每半年在欧洲举行的Seminaire Lotharingien de Combinatoire，并与来自世界各国的许多外国研究人员就代数组合学和相关领域的几个主题交换信息和进行讨论。2005年，我们资助了克劳德·伯纳德·李大学卡米尔·乔丹学院的蒋增教授 ...更多信息 1日访问日本三周。我们讨论了很多关于Andrews-Stanley配分函数和Al-Salam-Chihara多项式，并一起参加了在京都举行的组合表示论世界会议和在静冈举行的表示论研讨会。我们还访问了东京大学的寺田板樽教授，并在东京大学作了讲座。我和江增教授在京都的论坛上各作了一次报告。我也有机会访问学院卡米尔约旦，大学克劳德伯纳德里昂1几次在场合出席会议Seminaire Lotharingien德Combinatoire，给了会谈正交多项式和平面分区在Combinatoire等理论之Nombres。我们还讨论了弗雷德里克·约赫特和阿尼斯Kasraoui对霍尔-利特尔伍德多项式和罗杰-拉马努金类型的身份，或统计有序分区集和q-斯特林数。在全对称自补平面分拆的精化计数的Mills-Robins-拉姆西图上也取得了进展。这些问题已经公开了二十多年，吸引了许多与交错符号矩阵相关的研究者的兴趣。最后，我们要对冈田硕治教授和阿兰·拉斯库教授提出的宝贵意见和建议表示深切的感谢。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