当k≤10时区传递6-(v,k,λ)设计的存在性

On the Existence of Block-trancitive 6-(v,k,λ) Designs with k≤10

在有限关联结构的研究中,设计的传递性是一个非常重要的研究对象.近年来,有许多关于旗传递t-设计的研究,然而对于区传递的研究并不多,尤其是当t较大(即t≥4)时,就更少了.P.J.Cameron与C.E.Praeger证明了:如果D是一个区传递t-设计,那么t≤7.并且猜想:不存在非平凡的区传递6-设计.文中,我们限制参数k≤10,证明了在这种特殊的情况下猜想的正确性.

Among studying the finite incidence structures,the transitivity is an important research object.In recent years,there have been a great deal of research concerning with the flag-transitive t-designs.However,few research about the block-transitive t-designs with large,i.e.t≥4.P.J.Cameron and C.E.Praeger showed that if D is a block-transitive t-design then t≤7 and conjectured there are no nontrivial block-transitive 6-designs.In this paper,we considered the special case of the conjecture with block size k≤10,and proved that this conjecture is correct for k≤10.