论文标题
在几个顶点上的三元组合中的协会方案
Association schemes on triples over few vertices
论文作者
论文摘要
在本文中，我们获得了经典关联方案的较高维度类似物的分类结果，称为三倍（ASTS）上的关联方案。我们提出了一种算法，该算法列举了固定数量的顶点上的所有AST，其在某些组的作用下是非平凡关系是不变的。将此算法应用于三个，四个和五个顶点以及适当的小组动作，产生了三个顶点的独特AST，即四个或五个顶点的独特对称AST，这是两个具有两个非平凡关系的独特的AST，以及在五个顶点上具有唯一的非琐事循环AST。
In this paper, we obtain classification results for higher-dimensional analogues of classical association schemes called association schemes on triples (ASTs). We present an algorithm that enumerates all ASTs on a fixed number of vertices whose nontrivial relations are invariant under the action of some group. Applying this algorithm to three, four, and five vertices along with appropriate group actions yields the unique AST over three vertices, the unique symmetric ASTs over four or five vertices, the unique AST over four vertices with two nontrivial relations, and the unique nontrivial circulant AST over five vertices.
