论文标题
在某些类别的矩形设计上
On certain classes of rectangular designs
论文作者
论文摘要
矩形设计被归类为常规，拉丁常规，半毛，拉丁半界和奇异设计。使用属于上述类的矩阵方法获得了一些系列的自我和字母隔离设计。在每种结构中，我们都会获得一个矩阵N，其块为正方形（0,1）矩阵，因此n成为矩形设计的入射矩阵。该方法是已知设计的发射矩阵的众所周知的战术分解的逆转。作者已经使用此方法获得了一些系列的群体和拉丁正方形设计。战术可分解设计引起了人们的极大兴趣，因为它们与设计的自动形态有联系，请参见Bekar等。 （1982）。此处构建的矩形设计既具有统计和联合利益。
Rectangular designs are classified as regular, Latin regular, semiregular, Latin semiregular and singular designs. Some series of selfdual as well as alpharesolvable designs are obtained using matrix approaches which belong to the above classes. In every construction we obtain a matrix N whose blocks are square (0,1) matrices such that N becomes the incidence matrix of a rectangular design. The method is the reverse of the well known tactical decomposition of the incidence matrix of a known design. Authors have already obtained some series of Group Divisible and Latin square designs using this method. Tactical decomposable designs are of great interest because of their connections with automorphisms of designs, see Bekar et al. (1982). The rectangular designs constructed here are of statistical as well as combinatorial interest.
