An improvement on H design
An improvement on H design
复制标题
DOI：
10.1002/jcd.20184
复制
发表时间：
2009-01
影响因子：
0.7
通讯作者：
L. Ji
中科院分区：
文献类型：
--
作者：
L. Ji
一个H（m，g，4，3）是一个三元组$（X，\cal T，\cal B）$，其中X是mg点的集合，$\cal T$是X划分成m个大小为g的不相交集合，$\cal B$是$\cal T$的一组4元横截，使得$\cal T$的每个3元横截包含在其中一个中。这样的设计是由Hanani 2提出的，他用它来研究Steiner四重系统。米尔斯表明，对于$m > 3，m \not= 5$，一个H（m，g，4，3）存在当且仅当mg是偶数和$g（m-1）（m-2）$可被3整除，而对于$m=5$，一个H（5，g，4，3）存在，如果g可被4或6 10整除。在这篇文章中，我们将证明H（5，g，4，3）存在，如果g是偶数，$g \neq 2$和$g \not \equiv 10，26\，（{\rm mod}\，48）$。© 2008 Wiley Periodicals，Inc. J Combin Designs 17：25-35，2009
An H(m, g, 4, 3) is a triple $(X,\cal T,\cal B)$, where X is a set of mg points, $\cal T$ is a partition of X into m disjoint sets of size g, and $\cal B$ is a set of 4‐element transverses of $\cal T$, such that each 3‐element transverse of $\cal T$ is contained in exactly one of them. Such a design was introduced by Hanani 2 , who used it to study Steiner quadruple systems. Mills showed that for $m > 3, m \not= 5$, an H(m, g, 4, 3) exists if and only if mg is even and $g(m-1)(m-2)$ is divisible by 3, and that for $m=5$, an H(5, g, 4, 3) exists if g is divisible by 4 or 6 10 . In this article, we shall show that an H(5, g, 4, 3) exists if g is even, $g \neq 2$ and $g \not \equiv 10, 26\, ({\rm mod} \,48)$. © 2008 Wiley Periodicals, Inc. J Combin Designs 17: 25–35, 2009