Quasigroups and loops: Introduction by Hala O. Pflugfelder

By Hala O. Pflugfelder

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5 If n > 1, then 3 2n-. 5. 526753 . . ; in particular, F(n) > 4az" for n > 1. The proof of this is omitted. References [1] X. M. Chang, F. K. Hwang and J. F. Weng, Group testing with two and three defectives, Ann. N. Y. Acad. Sci. Vol. 576, Ed. M. F. Capobianco, M. Guan, D. F. Hsu and F. Tian, (New York, 1989) 86-96. [2] R. Dorfman, The detection of defective members of large populations, Ann. Math. Statist. 14 (1943) 436-440. [3] M. C. Hu, F. K. Hwang and J. K. Wang, A boundary problem for group testing, SIAM J.

F. Capobianco, M. Guan, D. F. Hsu and F. Tian, (New York, 1989) 86-96. [2] R. Dorfman, The detection of defective members of large populations, Ann. Math. Statist. 14 (1943) 436-440. [3] M. C. Hu, F. K. Hwang and J. K. Wang, A boundary problem for group testing, SIAM J. AIg. Disc. Methods 2 (1981) 81-87. [4] F. K. Hwang, A minimax procedure on group testing problems, Tamkang J. Math. 2 (1971) 39-44. [5] F. K. Hwang, Hypergeometric group testing procedures and merging procedures, Bull. Inst. Math.

1, S -a S1 --^ S implies n S1 = S n {D1} # 0. This implies D1 E S n So. Since D1 ¢ S, S n So S. (iii) = (i): Trivially true by using the definition of realizability. 3 Li ' s s-Stage Algorithm Li [12] extended a 2-stage algorithm of Dorfman [2] (for PGT) to s stages . At stage 1 the n items are arbitrarily divided into gl groups of k, ( some possibly k, - 1) items. Each of these groups is tested and items in pure groups are identified as good and removed. Items in contaminated groups are pooled together and arbitrarily redivided into g2 groups of k2 (some possibly k2 - 1) items; thus entering stage 2.

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