Existence of a-fold Perfect （v, {5, 8}, 1）-Mendelsohn Designs

• Published in: Acta mathematica Sinica. English series no. 3; pp. 445 - 464
• Main Author: Ming Xiao XIANG Yun Qing XU Frank E. BENNETT
• Format: Journal Article
• Language: English
• Published: 2010
• Subjects: Mendelsohn设计; PMD; 医学博士; 周期性排列; 正整数集
• ISSN: 1439-8516; 1439-7617

Let v be a positive integer and let K be a set of positive integers. A （v, K, 1）-Mendelsohn design, which we denote briefly by （v, K, 1）-MD, is a pair （X, B） where X is a v-set （of points） and B is a collection of cyclically ordered subsets of X （called blocks） with sizes in the set K such that every ordered pair of points of X are consecutive in exactly one block of B. If for all t =1, 2,..., r, every ordered pair of points of X are t-apart in exactly one block of B, then the （v, K, 1）-MD is called an r-fold perfect design and denoted briefly by an r-fold perfect （v, K, 1）-MD. If K = {k） and r = k - 1, then an r-fold perfect （v, （k）, 1）-MD is essentially the more familiar （v, k, 1）-perfect Mendelsohn design, which is briefly denoted by （v, k, 1）-PMD. In this paper, we investigate the existence of 4-fold perfect （v, （5, 8}, 1）-Mendelsohn designs.