✦ LIBER ✦

Designs with no three mutually disjoint blocks

✍ Scribed by A. Baartmans; Mohan Shrikhande

Publisher: Elsevier Science
Year: 1982
Tongue: English
Weight: 759 KB
Volume: 40
Category: Article
ISSN: 0012-365X
DOI: 10.1016/0012-365x(82)90114-5

No coin nor oath required. For personal study only.

✦ Synopsis

Let D(u, b, r, k, A) be any quasi-symmetric block design with block intersection numbers 0 and y. Suppose D has no three mutually disjoint blocks. We show ttcat for a given value of y, there are only finitely many parameter sets of such designs. Moreover, the 'extremal' &signs D have one of the following parameter sets: (1) u=4y, k=2y,A=2y-1 (ys2) (2) u=y(y*+3y+l), k=y(y+l), A=y*+y-1 (~32) (3) u=(y+l)(y*+2y-l), k=y(y+l),A=y*(ya2) A computer search revealed only three parameter sets in the range 1 d y G 199, which are not of the above types.

1. Hntroduction

Let P be a set of elements (points) and @I be

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