Incomplete Group Divisible Designs with Block Size Four and General Index  

作　　者：Li-dong Wang Hai-rong Kong Hong-juan Liu 

机构地区：[1]Department of Basic Courses, Chinese People's Armed Police Force Academy, Langfang 065000, China [2]School of Science, Hebei University of Technology, Tianjin 300401, China [3]Department of Computer Science and Engineering, Langfang Polytechnic Institute, Langfang 065000, China

出　　处：《Acta Mathematicae Applicatae Sinica》2011年第3期407-418,共12页应用数学学报（英文版）

基　　金：Supported by the National Natural Science Foundation of China (No. 10571043, 10771051, 11001182, 10901051)

摘　　要：In this paper, we investigate the existence of incomplete group divisible designs （IGDDs） with block size four, group-type （g, h） u and general index λ. The necessary conditions for the existence of such a design are that u ≥ 4, g ≥ 3h, λg（u 1） ≡ 0 （mod 3）, λ（g h）（u 1） ≡ 0 （mod 3）, and λu（u 1）（g 2 h 2 ） ≡ 0 （mod 12）. These necessary conditions are shown to be sufficient for all λ≥ 2. The known existence result for λ = 1 is also improved.In this paper, we investigate the existence of incomplete group divisible designs （IGDDs） with block size four, group-type （g, h） u and general index λ. The necessary conditions for the existence of such a design are that u ≥ 4, g ≥ 3h, λg（u 1） ≡ 0 （mod 3）, λ（g h）（u 1） ≡ 0 （mod 3）, and λu（u 1）（g 2 h 2 ） ≡ 0 （mod 12）. These necessary conditions are shown to be sufficient for all λ≥ 2. The known existence result for λ = 1 is also improved.

关 键 词：group divisible design incomplete group divisible design holy group divisible design 

分 类 号：O156.1[理学—数学] TG139.8[理学—基础数学]