For a positive integer k, we say that an association scheme \((\varOmega ,S)\) is k-equivalenced if each non-diagonal element of S has valency k. An association scheme \((\varOmega ,S)\) is called Frobenius when the set S is equal to the set of orbitals of a Frobenius group G on a finite set \(\varOmega \). It is known that every k-equivalenced association scheme is Frobenius when k=2, 3. In this paper, we show that every 4-equivalenced association scheme is Frobenius, and give some properties of a 4-equivalenced association scheme.

中文翻译：

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每四个等效的协会计划都是Frobenius

对于正整数ķ，我们说的关联方案\（（\ varOmega，S）\）是ķ -等效的，如果各非对角元素小号具有化合价ķ。当集合S等于有限集\（\ varOmega \）上的Frobenius群G的轨道集时，关联方案\（（\ varOmega，S）\）被称为Frobenius 。已知当k时，每个k等价的关联方案都是Frobenius= 2，3。在本文中，我们证明了每个4个等价的关联方案都是Frobenius，并给出了4个等价的关联方案的一些性质。