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Synthetic study of algebraic combinatorics

代数组合学的综合研究

基本信息

批准号：
16340010
负责人：
BANNAI Eiichi
金额：
$ 11.2万
依托单位：
Kyushu University
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (B)
财政年份：
2004
资助国家：
日本
起止时间：
2004 至 2007
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-16340010/
关键词：
algebraic combinatorics association scheme design code modular form spherical design lattice coherent configuration アソシエーションスキー Moonshine 球面デザイン Sphere packing 距離正則グラフ sphece packing

项目摘要

One of the goal of this grant was to widely contribute to the advancement of algebraic combinatorics in Japan through the financial support for conferences and workshops. During the fiscal year 2004-2007, the grant was used to partly support The 21st, 22nd, 23rd, 24th Algebraic Combinatoric Symposiums(Shinshu University, Ehime University, Tobhiku University, Ehime University), annual symposiums at RIMS, two COE Workshops on Sphere Packings, held at Kyushu University, and Mini-symposiums on algebraic combinatorics(three at Kyushu university and one in Kobegakuin University), etc. We also held 4 Japan-Korea workshops on Algebra and Combinatorics, and contributed to the international relations and cooperations.Research in Algebraic Combinatorics in Japan is showing steady progress. The progress covers diverse areas such as distant-regular graphs, association schemes, codes, designs, lattices, modular forms. The recent research of the principal investigator is focused on the study of Eucli … More dean designs. Collaborating with Etsuko Bannai, we obtained the classification of tight 4-designs with constant weight, the classification of Gaussian tight 4-designs, and the classification of optimal tight 4-designs on two concentric spheres. In addition, jointly with Suprijanto, we succeeded in showing that we can get new tight Euclidean designs starting from some tight Euclidean designs. Our recent work includes the classification of tight Euclidean 7-designs on two concentric spheres. We have also proved that any antipodal t-design of degree s with t$2s-3 has the structure of Q-polynomial association scheme, and found such new examples with t=5 and s=4 from maximal real MUB. We started to study how coherent configurations are attached to tight Euclidean designs. We succeeded in proving the uniqueness of two association schemes related to universally optimal codes in the sense of H. Cohn (Bannai-Bannai-Bannai), and have shown, jointly with Abdukhalikov and Suda, that higher dimensional analogues of one of them are obtained from maximal real MUB. Less

这笔赠款的目标之一是通过对会议和讲习班的财政支持，广泛促进日本代数组合学的发展。在2004-2007财政年度，该赠款用于部分支持第21、22、23和24届代数组合学研讨会（信州大学、爱媛大学、东比大学、爱媛大学）、RIMS年度研讨会、在九州大学举办的两次COE球形填充研讨会以及代数组合学小型研讨会（九州大学3所，神户学院大学1所）等。此外，还举办了4次日韩间的代数学、组合学研讨会，为国际交流与合作做出了贡献。这些进展涵盖了不同的领域，如距离正则图，关联方案，代码，设计，格，模形式。首席研究员最近的研究集中在对欧几里得的研究上 ...更多信息迪恩设计。与Etsuko Bannai合作，我们得到了具有常数权重的紧4-设计的分类，高斯紧4-设计的分类，以及两个同心球上的最优紧4-设计的分类。此外，与Suprijanto一起，我们成功地证明了我们可以从一些紧欧几里得设计开始得到新的紧欧几里得设计。我们最近的工作包括两个同心球上紧欧氏7-设计的分类。证明了任意t = 2s-3的s次对映t-设计都具有Q-多项式结合方案的结构，并从极大真实的MUB中找到了t=5和s=4的新例子.我们开始研究如何将相干构型与紧欧几里得设计联系起来。我们成功地证明了两个关于H意义下泛最优码的结合方案的唯一性。Cohn（Bannai-Bannai-Bannai），并与Abdukhalikov和苏达一起证明，其中一个的高维类似物可以从最大真实的MUB中获得。少