| λ≤5的区传递7-(v,k,λ)设计的存在性 |
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| 引用本文： | 龚罗中,刘伟俊. λ≤5的区传递7-(v,k,λ)设计的存在性[J]. 浙江大学学报(理学版), 2013, 40(4): 378-381 |
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| 作者姓名： | 龚罗中 刘伟俊 |
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| 作者单位： | [1]湖南科技学院数学与计算科学系,湖南永州425100 [2]中南大学统计学院,湖南长沙410075 |
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| 基金项目： | Supported by Scientific Research Fund of Hunan Provincial Education Department（Grant No.12B050）; NNSFC（Grant No.11271208） |
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| 摘 要： | 1993年，CAMERON和PRAGEGER证明了不存在t>7的非平凡的区传递t-设计，并且猜想不存在非平凡的区传递6设计.然而区传递7-设计的存在性仍然是一个公开的问题.本文研究了这一公开问题，证明了当λ≤5时不存在非平凡的区传递7-（v,k,λ）设计.
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| 关 键 词： | font-family: 宋体,font-size: 10.5pt,mso-bidi-font-family: 宋体,mso-ansi-language: EN-US,mso-fareast-language: ZH-CN,mso-bidi-language: AR-SA" >设计, 区传递, EN-US" > Cameron- EN-US" >Preager猜想, |
| 收稿时间： | 2012-04-28 |
The existence of block transitive 7-(v,k,λ) designs with λ≤5 |
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| GONG Luo-zhong,LIU Wei-jun. The existence of block transitive 7-(v,k,λ) designs with λ≤5[J]. Journal of Zhejiang University(Sciences Edition), 2013, 40(4): 378-381 |
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| Authors: | GONG Luo-zhong LIU Wei-jun |
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| Affiliation: | 1. Deportment of Mathematics and Computing, Hunan University of Science and Engineering, Yongzhou 425100, Hunan Province, China; 2. College of Statistics, Central South University, Changsha 410075, China) |
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| Abstract: | In 1993, CAMERON and PRAEGER proved that there are no nontrivial block-transitive t-designs with t 〉7 and conjectured that there are no nontrivial block-transitive 6-designs. But the existence of block-transitive 7-de- signs is still an open problem. In this paper, this open problem is studied and the fact that there are no nontrivial block-transitive 7-（v,k,λ） designs with λ≤5 is proved. |
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| Keywords: | design block-transitive Cameron-Preager conjecture |
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