✦ LIBER ✦

Completely regular designs

✍ Scribed by William J. Martin

Publisher: John Wiley and Sons
Year: 1998
Tongue: English
Weight: 215 KB
Volume: 6
Category: Article
ISSN: 1063-8539
DOI: 10.1002/(sici)1520-6610(1998)6:4<261::aid-jcd4>3.0.co;2-d

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✦ Synopsis

We study a class of t-designs which enjoy a high degree of regularity. These are the subsets of vertices of the Johnson graph which are completely regular, in the sense of Delsarte [Philips Res. Reports Suppl. 10 (1973)]. After setting up the basic theory, we describe the known completely regular designs. We derive very strong restrictions which must hold in order for a design to be completely regular. As a result, we are able to determine which symmetric designs are completely regular and which Steiner systems with t = 2 are completely regular.

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