Large sets of Kirkman triple systems of orders 2(2n+1)+1
Large sets of Kirkman triple systems of orders 2(2n+1)+1
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大组柯克曼三阶系统 2(2n 1) 1
DOI：
10.1016/j.disc.2021.112373
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发表时间：
2021
影响因子：
0.8
通讯作者：
Ji Lijun
中科院分区：
文献类型：
--
作者：
Xu Juanjuan;Ji Lijun
Kirkman三系大集的存在性问题是设计理论中的一个老问题，至今仍未得到解决。本文利用（2，1）-RSQS（4 n）构造了一个LKTS（22 n+ 1+ 1），它具有良好的结构，并用于构造基于3-平衡设计的任意非负整数m和n的LKTS（6 <$5m（4 <$5n + 1）±3）.
The existence of large set of Kirkman triple systems (LKTSs) is an old problem in design theory, which is still far from settled. In this paper, we use a (2, 1)-RSQS∗(4 n) to construct an LKTS (2 2 n+ 1+ 1), which has a nice structure and is used to construct an LKTS (6⋅ 5 m (4⋅ 5 n+ 1)±3) for any nonnegative integers m and n based on 3-wise balanced designs.