| 谭琼华,黄宠辉.当k≤10时区传递6-(v,k,λ)设计的存在性[J].南华大学学报(自然科学版),2010,24(4):74~76.[TAN Qiong-hua1,2,HUANG Chong-hui1.On the Existence of Block-trancitive 6-(v,k,λ) Designs with k≤10[J].Journal of University of South China(Science and Technology),2010,24(4):74~76.] |
| 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 |
| 投稿时间：2010-07-06 |
| DOI： |
| 中文关键词: 区传递 t-设计 3-齐次 自同构. |
| 英文关键词:Block-transitive t-designs 3-homogeneous automorphism. |
| 基金项目:国家自然科学基金资助项目(10871205) |
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| 中文摘要: |
| 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. |
| 英文摘要: |
| 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. |
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