Existence of 4-fold Perfect (v, {5, 8}, 1)-Mendelsohn Designs  

作　　者：Ming Xiao XIANG Yun Qing XU Frank E. BENNETT 

机构地区：[1]Department of Mathematics, Ningbo University, Ningbo 315211, P. R. China [2]Department of Mathematics, Mount Saint Vincent University, Halifax, Nova Scotia B3M 2J6, Canada

出　　处：《Acta Mathematica Sinica,English Series》2010年第3期445-464,共20页数学学报（英文版）

基　　金：supported by National Natural Science Foundation of China (Grant No.60873267);Zhejiang Provincial Natural Science Foundation of China (Grant No. Y607026); sponsored by K. C. Wong Magna Fund in Ningbo University;the third author is supported by NSERC Grant OGP 0005320

摘　　要：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.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.

关 键 词：Mendelsohn design transversal design group divisible desiga 

分 类 号：O157.2[理学—数学] S763.712.4[理学—基础数学]