Existence of 4-fold perfect (v,{5,8},1)- Mendelsohn design
首发时间:2008-07-16
Abstract: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.
keywords: Mendelsohn designs;transversal design;Group divisible design
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4-重完美(v,{5,8},1)-MD 的存在性
摘要:令v是正整数,K是正整数集,(v,K,1)-Mendelsohn设计,简记为(v,K,1)-MD 是对集(X,B) 其中X是v-点的集合,B是循环有序集X(称区组)的子集,大小集合为K,使得X中每一有序对在B中恰出现一次,如果对所有的t=1,2,...,r, X中的每一有序在B中恰t-分离一次,那么(v,K,1)-MD称为r-重完美设计,记为r-重完美(v,K,1)-MD. 如果K={k},r=k-1,那么r-重完美(v,{k},1)-MD 实质上就是(v,k,1)-完美Mendelsohn设计,简记为(v,k,1)-PMD,在这篇文章中,我们将研究4-重完美(v,{5,8},1)-MD 的存在性。
关键词: Mendelsohn设计 截态设计 分组设计
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No.2290420596412161****
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