组合C_(n)^(m)循环生成法在柯克曼三元系中的应用

Applicaton of C_(n)^(m) Loop Generation Method in Kirkman Triple System

柯克曼女生散步问题是组合设计中的传统问题,提出组合C_(n)^(m)的循环生成法。此方法将集合V中n个元素均匀分布在圆周上,将求解C_(n)^(m)的组合转换为在圆周上求解m边形组合,一个m边形沿着圆周转动可产生n个结构相同的m边形。当m=3,v≡3 mod 12时,把组合C_(n)^(m)的循环生成法运用于构造柯克曼三元系,可方便生成构造柯克曼三元系。

Kirkman Schoolgirl Problem is a traditional problem in Combinatorial Design. This paper pro poses C_(n)^(m)Loop generation method, and n elements are marked as points on the circle in this method. The combination of C_(n)^(m)is converted to solving m-shaped polygons on the circle, and an m-shaped polygon rotating along the circle can generate n m-shaped polygons with the same structure. When m=3, v≡3mod 12, C_(n)^(m)Loop generation method is applied to construct the Kirkman Triple system, which can construct the Kirkman Triple system easily.