Super-Simple Holey Steiner Pentagon Systems and Related Designs † R. Julian R. Abel, 1 Frank E. Bennett, 2 Gennian Ge 3 1 School of Mathematics and Statistics, University of New South Wales, Sydney, NSW 2052, Australia, E-mail: julian@maths.unsw.edu.au 2 Department of Mathematics, Mount Saint Vincent University, Halifax, NS B3M 2J6, Canada, E-mail: Frank.Bennett@msvu.ca 3 Department of Mathematics, Zhejiang University, Hangzhou 310027, Zhejiang, P.R. China, E-mail: gnge@zju.edu.cn Received February 13, 2007; revised July 25, 2007 Published online 14 September 2007 in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/jcd.20171 Abstract: A Steiner pentagon system of order v (SPS(v)) is said to be super-simple if its under- lying (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 Keywords: super-simple; BIBD; GDD; Steiner pentagon system; Holey Steiner pentagon system; Primary 05B05 1. INTRODUCTION Let K n be the complete undirected graph with n vertices. A pentagon system (PS) of order n is a pair (K n , B), where B is a collection of edge-disjoint pentagons which partition the Contract grant sponsor: Natural Sciences and Engineering Research Council of Canada (to F. E. B.); Contract grant number: NSERC OGP 0005320; Contract grant sponsor: Natural Science Foundation of China (to G. G.); Contract grant number: 10771193; Contract grant sponsor: Zhejiang Provincial Natural Science Foundation (to G. G.); Contract grant number: R604001; Contract grant sponsor: Program for New Century Excellent Talents in University (to G. G.). † A portion of this research was carried out while the second author was visiting the University of New South Wales in July of 2006. Journal of Combinatorial Designs © 2008 Wiley Periodicals, Inc. 301