Graphs and association schemes: higher-dimensional invariants and their applications

1. 我们与圣彼得堡Steklov数学研究所的Ilia Ponomarenko和海南大学的Jin Guo合作，确定了排列图的Weisfeiler-Leman维数的上界。文件正在准备提交。在与Sho Suda（国防学院）的合作中，我们证明了Witt 11设计自然产生的某种关联方案是由其Bose-Mesner代数的结构常数唯一决定的。这篇论文正在审查中。在与Vladislav Kabanov （Krasovskii数学研究所）的合作中，我们研究了可分解为可分割的设计图和delsat - hoffman柯克的强正则图的多产构造。这篇论文正在准备提交。

1. In collaboration with Ilia Ponomarenko (Saint-Petersburg department of the Steklov Institute of Mathematics) and Jin Guo (Hainan University), we determined the upper bound on the Weisfeiler-Leman dimension of permutation graphs. The paper is being prepared for submission.2. In collaboration with Sho Suda (National Defence Academy), we showed that a certain association scheme naturally arising from the Witt 11-design is uniquely determined by the structure constants of its Bose-Mesner algebra. The paper is under review.3. In collaboration with Vladislav Kabanov (Krasovskii Institute of Mathematics), we studied a prolific construction of strongly regular graphs that are decomposable into divisible design graphs and a Delsarte-Hoffman coclique. The paper is being prepared for submission.