区传递点非本原2-设计的Delandtsheer-Doyen参数
Delandtsheer--Doyen parameters for block-transitive point-imprimitive 2-designs
摘要：
Delandtsheer和Doyen用区组大小来界定点非本原区组传递2-设计的点数。为此，他们引入了两个整数参数，m和n，现在称为Delandtsheer-Doyen参数，将块大小与点上相关的不变性系统的参数联系起来。我们表明，Delandtsheer-Doyen参数提供上界上的置换秩的不相容性系统和一类系统上引起的群体。我们探讨极端的情况下，这些界限的实现，给出了一个新的家庭建设的设计实现这些界限，并提出了几个悬而未决的问题Delandtsheer-Doyen参数。
英文摘要：
Delandtsheer and Doyen bounded, in terms of the block size, the number of points of a point-imprimitive, block-transitive 2-design. To do this they introduced two integer parameters, m and n, now called Delandtsheer--Doyen parameters, linking the block size with the parameters of an associated imprimitivity system on points. We show that the Delandtsheer--Doyen parameters provide upper bounds on the permutation ranks of the groups induced on the imprimitivity system and on a class of the system. We explore extreme cases where these bounds are attained, give a new construction for a family of designs achieving these bounds, and pose several open questions concerning the Delandtsheer--Doyen parameters.
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