Super-simple holey Steiner pentagon systems and related designs

✍ Scribed by R. Julian R. Abel; Frank E. Bennett; Gennian Ge

• Publisher: John Wiley and Sons
• Year: 2008
• Tongue: English
• Weight: 256 KB
• Volume: 16
• Category: Article
• ISSN: 1063-8539
• DOI: 10.1002/jcd.20171

✦ Synopsis

Abstract

A Steiner pentagon system of order v (SPS(v)) is said to be super‐simple if its underlying (v, 5, 2)‐BIBD is super‐simple; that is, any two blocks of the BIBD intersect in at most two points. It is well known that the existence of a holey Steiner pentagon system (HSPS) of type T implies the existence of a (5, 2)‐GDD of type T. We shall call an HSPS of type T super‐simple if its underlying (5, 2)‐GDD of type T is super‐simple; that is, any two blocks of the GDD intersect in at most two points. The existence of HSPSs of uniform type h^n^ has previously been investigated by the authors and others. In this article, we focus our attention on the existence of super‐simple HSPSs of uniform type h^n^. © 2007 Wiley Periodicals, Inc. J Combin Designs 16: 301–328, 2008