Block transitive Steiner systems with more than one point orbit

✍ Scribed by David M. Evans

• Book ID: 102307490
• Publisher: John Wiley and Sons
• Year: 2004
• Tongue: English
• Weight: 101 KB
• Volume: 12
• Category: Article
• ISSN: 1063-8539
• DOI: 10.1002/jcd.20018

✦ Synopsis

Abstract

For all ‘reasonable’ finite t, k, and s, we construct a t‐(ℵ~0~, k, 1) design and a group of automorphisms which is transitive on blocks and has s orbits on points. In particular, there is a 2‐(ℵ__0__, 4, 1) design with a block‐transitive group of automorphisms having two point orbits. This answers a question of P. J. Cameron and C. E. Praeger. The construction is presented in a purely combinatorial way, but is a by‐product of a new way of looking at a model‐theoretic construction of E. Hrushovski. © 2004 Wiley Periodicals, Inc.