区组长为奇素数的自反MD设计 (英)

Self-converse Mendelsohn Designs with Odd Prime Block Size

中文关键词:  自反MD设计  差圈  SDC  UDC  CDC.

英文关键词:self-converse Mendelsohn design  difference cycle  SDC  UDC  CDC.

中文摘要:

      本文利用差方法对自反MD设计SCMD$(4mp, p,1)$的存在性给出了构造性证明, 这里$p$为奇素数, $m$为正整数.

英文摘要:

      A Mendelsohn design $\MD(v, k, \lambda)$ is a pair $(X,{\cal B}),$ where $X$ is a $v$-set and ${\cal B}$ is a collection of $k$-tuples from $X$ such that each ordered pair from $X$ is contained in exactly $\lambda$ $k$-tuples of ${\cal B}$. An $\MD(v, k, \lambda)$ is called self-converse and denoted by $\SCMD(v, k, \lambda)=(X, {\cal B}, f)$, if there exists an isomorphic mapping $f$ from $(X, {\cal B})$ to $(X, {\cal B}^{-1})$. In this paper, using difference method, we give a constructive proof for the existence of $\SCMD(4mp,p,1),$ where $p$ is an odd prime and $m$ is a positive integer.