The Construction of Pairwise Additive Minimal BIB Designs with Asymptotic Results  

作　　者：Kazuki Matsubara Sanpei Kageyama 

机构地区：[1]Graduate School of Science, Hiroshima University, Higashi-Hiroshima, Japan [2]Hiroshima Institute of Technology, Hiroshima, Japan

出　　处：《Applied Mathematics》2014年第14期2130-2136,共7页应用数学（英文）

摘　　要：An asymptotic existence of balanced incomplete block (BIB) designs and pairwise balanced designs (PBD) has been discussed in [1]-[3]. On the other hand, the existence of additive BIB designs and pairwise additive BIB designs with k = 2?and?λ = 1?has been discussed with direct and recursive constructions in [4]-[8]. In this paper, an asymptotic existence of pairwise additive BIB designs is proved by use of Wilson’s theorem on PBD, and?also for some l?and k the exact existence of l?pairwise additive BIB designs with block size k and?λ = 1?is discussed.An asymptotic existence of balanced incomplete block (BIB) designs and pairwise balanced designs (PBD) has been discussed in [1]-[3]. On the other hand, the existence of additive BIB designs and pairwise additive BIB designs with k = 2?and?λ = 1?has been discussed with direct and recursive constructions in [4]-[8]. In this paper, an asymptotic existence of pairwise additive BIB designs is proved by use of Wilson’s theorem on PBD, and?also for some l?and k the exact existence of l?pairwise additive BIB designs with block size k and?λ = 1?is discussed.

关 键 词：Incidence Matrix Pairwise BALANCED DESIGN (PBD) BALANCED Incomplete Block DESIGN (BIBD) ADDITIVE BIB DESIGN Pairwise ADDITIVE BIB DESIGN Wilson’s Theorem 

分 类 号：O1[理学—数学]