19阶Steiner三连系的构造与计数

Construction and Enumeration of Steiner Triple Systems of Order 19

阐明了19阶Steiner三连系构造的基本思路.给出了边矩阵的定义,先将边矩阵分解为完全图和完全三分图,然后将完全图和完全三分图分别分解,得到Steiner三连系,提出了基于Kv的子图分解的Steiner三连系的构造方法和计数方法.用2种方案具体给出19阶Steiner三连系的构造过程和计数.结果表明:文中的Steiner三连系的构造方法和计数方法是有效的,对Steiner三连系的构造方法和计数方法具有可推广性.

This paper clarified the basic idea of structure 19 orders Steiner triple systems. The definition of edge matrix was given, which can be decomposed into complete graph and complete triple graph. Then the complete graph and complete triple graph can be decomposed respectively to obtain Steiner triple systems. Based on the K~ sub graph decomposition, the enumeration method and construction method of Steiner triple systems were given. And two methods were used to give the specific construction processes and count of 19 orders Steiner triple systems. It can be concluded that the construction method and enu- meration method of Steiner triple systems are effective.