两类单纯3-设计的存在性
2021-12-30魏乐乐李伟霞
魏乐乐 李伟霞
4 结论
本文给出了以为自同构群的,区组长度为2d和2d+2(d≠5)的单纯3—设计的有关结果。令B为X的2d+2-子集,当d=5时,根据现有的方法无法判断B为类型(3)还是类型(5)的子群,因此在本文中d=5的情形没有被解决。
参考文献
[1]BIGGES N L,WHITE A T. Permutation groups and combinatoral structures[M]. Cambrige: Cambrige University Press, 1979.
[2]CAMERON P J, MAIMANI H R, OMIDI G R, et al. 3—designs from PSL(2,q)[J]. Discrete Mathematics, 2006, 306(23): 3063-3073.
[3]KERANEN M S, KREHER D L. 3-designs of PSL(2,2n) with block sizes 4 and 5[J]. Journal of Combinarorial Designs, 2004, 12(2): 103-111.
[4]LI W X, SHEN H. Simple 3-designs of PSL(2,2n) with block size 6[J]. Discrete Mathematics, 2008, 308(14): 3061-3072.
[5]LI W X, SHEN H. Simple 3-designs of PSL(2,2n) with block size 7[J]. Journal of Combinarorial Designs, 2008, 16(1): 1-17.
[6]GONG L, FAN G. Simple 3-designs of PSL(2,2n) with block size 8[J]. Utilitas Mathematica, 2018, 106: 3-9.
[7]李偉霞. 区组长度为2n-1因子的单纯3-设计[J]. 上海交通大学学报,2007,41(5):845-847.
[8]LI W X, SHEN H. Simple 3-designs with block size d+1 from PSL(2,2n) where d|(2n-1)[J]. Australasian Journal of Combinatorics,2011,51:235-241.
[9]魏乐乐,李伟霞. PSL(2,2n)与单纯3-(2n+1,2ld+1,λ)设计[J]. 理论数学,2019,9(4):540-545.
[10] DICKSON L E. Linear groups with an exposition of the Galois field theory[M]. New York: Dover Publications, 1958.