PSL(2,2n)与单纯3-(2n + 1,2ld + 1,λ)设计(l为奇数，d|(2n - 1)且d ≥ 3)
PSL(2,2n) and Simple 3-(2n + 1,2ld + 1,λ) Designs Where l Is Odd, d|(2n - 1) and d ≥ 3
摘要: 令X=GF(q)∪｛∞｝是射影直线。设l为奇数，d为满足d丨（2n-1）且d ≥ 3的正整数。本文确定了以PSL(2,2n)为自同构群，区组长度为2ld + 1，初始区组的稳定子群中含有d阶元的单纯3-设计的参数，并计算了构成这一参数的轨道的条数。利用PSL(2,2n)在X上作用的轨道，得到如下结论：这类单纯3-设计的参数为3-(2n + 1,2ld + 1，2l（2ld-1）（2ld+1）），构成这一设计的轨道的条数为。
Abstract: Let X=GF(q)∪｛∞｝ be the projective line. Let l be an odd integer. The integer d satisfies d丨（2n-1） and d ≥ 3. In this paper, we determined the parameter set of simple 3-designs from PSL(2,2n) with block size 2ld + 1 where the stabilizer of the initial block contains order d element of PSL(2,2n) and calculated the number of the orbits which form the simple 3-design with that pa-rameter set. By using the orbits of PSL(2,2n) on the X, the results show that the number of the orbits is which forms the simple 3-(2n + 1,2ld + 1，2l（2ld-1）（2ld+1）） design.
文章引用：魏乐乐, 李伟霞. PSL(2,2n)与单纯3-(2n + 1,2ld + 1,λ)设计(l为奇数，d|(2n - 1)且d ≥ 3)[J]. 理论数学, 2019, 9(4): 540-545. https://doi.org/10.12677/PM.2019.94071

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