α-可分解多部P_(3)-设计

α-Resolvable Multipartite P_(3)-Design

如果一个(m,n,3,λ)多部P_(3)-设计中的P_(3)区组可以划分为若干α-平行类,则称这个多部P_(3)-设计是α-可分解的。文章研究α-可分解(m,n,3,λ)多部P_(3)-设计的存在性,给出并证明其存在的充分必要条件为:(1)mn≥3,(2)αmn≡0(mod 3),(3)3λ(m-1)n≡0(mod 4α)。

If the P_(3) blocks in a(m,n,3,λ)multipart P_(3)-design can be divided into severalα-parallel classes,the multipart P_(3)-design is said to beα-Resolvable.The research is conducted on the existence ofα-Resolvable(m,n,3,λ)multipart P_(3)-designs.It is concluded that the necessary and sufficient condition for the existence is as follows:(1)mn≥3,(2)αmn≡0(mod 3),(3)3λ(m-1)n≡0(mod 4α).