无定形结合方案与配对融合的刻画
Characterizations of amorphic schemes and fusions of pairs
AI总结：
本文通过定义融合关系图，证明若该图连通但非路径则结合方案为无定形，并附带证明至多含一个非特定类型强正则关系的结合方案亦为无定形。
摘要：
若关系的每一种可能融合都能生成融合方案，则称该结合方案为无定形的。若融合一对关系能生成融合方案，则称该关系对为可融合的。我们在关系集上定义了融合关系图，若一对关系可融合则构成一条边。我们证明，若融合关系图连通但非路径，则该结合方案是无定形的。作为附带结果，我们证明若结合方案至多有一个关系既非Latin square型强正则也非negative Latin square型强正则，则它是无定形的。
英文摘要：
An association scheme is called amorphic if every possible fusion of relations gives rise to a fusion scheme. We call a pair of relations fusing if fusing that pair gives rise to a fusion scheme. We define the fusing-relations graph on the set of relations, where a pair forms an edge if it fuses. We show that if the fusing-relations graph is connected but not a path, then the association scheme is amorphic. As a side result, we show that if an association scheme has at most one relation that is neither strongly regular of Latin square type nor strongly regular of negative Latin square type, then it is amorphic.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
