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Matsubara, K. and Kageyama, S. (to be Published) The Existence of 3 Pairwise Additive for Any . Journal of Combinatorial Mathematics and Combinatorial Computing.

has been cited by the following article:

• TITLE: The Construction of Pairwise Additive Minimal BIB Designs with Asymptotic Results

  AUTHORS: Kazuki Matsubara, Sanpei Kageyama

  KEYWORDS: Incidence Matrix, Pairwise Balanced Design (PBD), Balanced Incomplete Block Design (BIBD), Additive BIB Design, Pairwise Additive BIB Design, Wilson’s Theorem

  JOURNAL NAME: Applied Mathematics, Vol.5 No.14, July 28, 2014

  ABSTRACT: 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 = 2andλ = 1has 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, andalso for some land k the exact existence of lpairwise additive BIB designs with block size k andλ = 1is discussed.