﻿ 三个组的G-设计 G-Design with Three Groups

Advances in Applied Mathematics
Vol.04 No.04(2015), Article ID:16421,4 pages
10.12677/AAM.2015.44045

G-Design with Three Groups

Li Zhu, Jian Wang

Nantong Vocational University, Nantong Jiangsu

Received: Nov. 2nd, 2015; accepted: Nov. 19th, 2015; published: Nov. 26th, 2015

Copyright © 2015 by authors and Hans Publishers Inc.

ABSTRACT

As a special example of the candelabra systems (CQS), G-design is the extension of group divisible designs (GD), which plays an important role in quadruple systems’ construction. With application of Stern and Lenz’s result on one-factorization of graphs, by direct construction, it is given that the sufficient and necessary condition for the existence of the G-design with three groups is that.

Keywords:t-Designs, Quadruple Systems, Candelabra Systems, G-Design

G-设计是可分组设计(GD)的推广，同时又是烛台型设计(CQS)的特例，它在四元系设计中起到重要作用。文章应用Stern和Lenz关于图因子分解的结论，通过直接构造法，得到具有三个组的G-设计存在的充分必要条件：

1. 引言

2. 预备知识

1)

2)

3)

4)

3. 主要结论

1)

2)

3)

4)

()；

{ }

(由引理2.2，图存在1-因子分解，记的1-因子分解，)。

()重复4次；

{ }

()重复2次；

{ }

()重复2次；

{ }

()重复2次；

{ }()；

{ }()。

{ } ()；

{ } ()。

()重复4次；

{ }

()重复2次；

{ }

()重复2次；

{ }()；

{ }()

{ }()

G-Design with Three Groups[J]. 应用数学进展, 2015, 04(04): 365-368. http://dx.doi.org/10.12677/AAM.2015.44045

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