Homogeneous and ultrahomogeneous Steiner systems

A Steiner system (or t  — ( v , k , 1) design) S is said to be homogeneous if, whenever the substructures induced on two finite subsets S 1 and S 2 of S are isomorphic, there is at least one automorphism of S mapping S 1 onto S 2 , and is said to be ultrahomogeneous if each isomorphism between the substructures induced on two finite subsets of S can be extended to an automorphism of S . We give a complete classification of all homogeneous and ultrahomogeneous Steiner systems. © 2003 Wiley Periodicals, Inc. J Combin Designs 11: 153–161, 2003; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/jcd.10034