Rank 5 association schemes and triality
Rank 5 association schemes and triality
复制标题
5级关联计划和试用
DOI：
10.1016/0024-3795(95)00102-w
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发表时间：
1995
影响因子：
1.1
通讯作者：
D. G. Higman
中科院分区：
文献类型：
--
作者：
D. G. Higman
具有秩为3的抛物线和满足一定一致性条件的corank为2的对称结合方案一方面可以解释为强正则设计（类似于对称设计），另一方面可以解释为几何。与群O+8（q）相关联的经典三重性提供了秩为3、余秩为2的抛物线的一族例子，并且零星的例子与群L3（4）、U6（2）和U3（5）相关联。triality例子和U3（5）例子被看作是标志传递的几何。结果包括一个特征的试验计划的参数水平上导致一个特征的计划使用结果的卡梅隆和德雷克，和证明（作为一个凯莱练习）的简单连接的例子与U3（5）。
Symmetric association schemes having a parabolic of rank 3 and corank 2 satisfying a certain uniformity condition can be interpreted on the one hand as linked strongly regular designs (analogous to linked symmetric designs) and on the other as geometries. Classical triality associated with the groups O+8(q) provides a family of examples with rank 3, corank 2 parabolics and sporadic examples are associated with the groups L3(4), U6(2) and U3(5). The triality examples and the U3(5) example are flag-transitive viewed as geometries. Results include a characterization on the level of parameters of the triality schemes leading to a characterization of the schemes using results of Cameron and Drake, and a proof (as a Cayley exercise) of simple connectivity of the example associated with U3(5).