Some self-blocking block designs

✍ Scribed by Dieter Jungnickel

• Publisher: Elsevier Science
• Year: 1989
• Tongue: English
• Weight: 834 KB
• Volume: 77
• Category: Article
• ISSN: 0012-365X
• DOI: 10.1016/0012-365x(89)90356-7

✦ Synopsis

To Haim Hanani on the occasion of his 75th birthday. Let D be a block design which has a blocking set. We call D self-blocking if the following two conditions hold: (i) The committees of D (i.e. the blocking sets of minimum cardinality of D) form a block design, which we denote by DC and (ii) The committees of DC are precisely the blocks of D. (We also say that D and DC are a pair of mutually blocking block designs, then.) We show that the classical projective planes PG(2, 9') are self-blocking; the same holds for PG(2,3)

and PG(2,5) as well as for the classical affine planes AG(2, q) with q 2 4.