On the Existence of (v,3×3,λ)-Splitting Balanced Incomplete Block Design with λ between 2 to 9  

作　　者：苏仁旺 王金华 

机构地区：[1]College of Statistics and Mathematics,Zhejiang Gongshang University [2]School of Science,Nantong University

出　　处：《Journal of Shanghai Jiaotong university(Science)》2008年第4期482-486,共5页上海交通大学学报（英文版）

基　　金：the National Natural Science Foundation of China (No. 10771193);the Starter Foundation for the Doctors of Zhejiang Gongshang University(No. 1020XJ030517);the Natural Science Foundationof Universities of Jiangsu Province (No. 07KJB110090);the Starter Foundation for the Doctors of Nantong University (No. 07B12)

摘　　要：Let （v, u × c,λ）-splitting BIBD denote a （v, u × c,λ）-splitting balanced incomplete block design of order v with block size u × c and index A. The necessary conditions for the existence of a （v, u × c,λ）-splitting BIBD are v ≥ uc, λ（v- 1） -- 0 0 mod （c（u- 1）） and Av（v- 1） - 0 mod （c^2u（u- 1））. In this paper, for 2 ≤λ≤ 9 the necessary conditions for the existence of a （v, 3 × 3, λ）-splitting BIBD are also sufficient with one possible exception for （v, λ） = （39, 9）.Let (v,u × c,λ)-splitting BIBD denote a (v,u × c,λ)-splitting balanced incomplete block design of order v with block size u × c and index λ. The necessary conditions for the existence of a (v,u × c,λ)-splitting BIBD are v uc, λ(v-1) ≡ 0 0 mod (c(u-1)) and λv(v-1) ≡ 0 mod (c2u(u-1)). In this paper, for 2 λ 9 the necessary conditions for the existence of a (v,3 × 3,λ)-splitting BIBD are also suffcient with one possible exception for (v,λ) = (39,9).

关 键 词：SPLITTING balanced incomplete block design group-divisible design （GDD） 

分 类 号：O157.2[理学—数学] TN911.22[理学—基础数学]