论文标题
Delandtsheer-用于块传递点象征2设计的doyen参数
Delandtsheer--Doyen parameters for block-transitive point-imprimitive 2-designs
论文作者
论文摘要
Delandtsheer和Doyen以块大小为边界，是点象征，块传播的2-Design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，将块大小与点上关联的不良性系统的参数联系起来。我们表明，delandtsheer- doyen参数在不限制系统和系统类别上引起的组的置换等级提供了上限。我们探讨了达到这些界限的极端情况，为达到这些界限的一系列设计提供了新的结构，并提出了有关Delandtsheer-doyen参数的几个开放问题。
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.
