The non-existence of certain skew-symmetric amorphous association schemes
The non-existence of certain skew-symmetric amorphous association schemes
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DOI：
10.1016/j.ejc.2010.04.004
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发表时间：
2009-09
期刊：
影响因子：
--
通讯作者：
Jianmin Ma
中科院分区：
文献类型：
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作者：
Jianmin Ma
一个关联方案是无定形的，如果它有尽可能多的融合方案。在代数层次上，Ivanov（1985）[12]对对称无定形格式进行了分类，Ito等人对交换无定形格式进行了分类。（1991）[11]。如果对角关系是唯一的对称关系，则称一个方案是斜对称的。我们证明了不存在的斜对称无定形计划，至少有四个类。我们还证明了非对称无定形格式是可交换的。
An association scheme is amorphous if it has as many fusion schemes as possible. At the algebraic level, symmetric amorphous schemes were classified by Ivanov (1985) [12] and commutative amorphous schemes were classified by Ito et al. (1991) [11]. A scheme is called skew-symmetric if the diagonal relation is the only symmetric relation. We show the non-existence of skew-symmetric amorphous schemes with at least four classes. We also prove that non-symmetric amorphous schemes are commutative.