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Homogeneous and ultrahomogeneous Steiner systems

✍ Scribed by Alice Devillers

Publisher
John Wiley and Sons
Year
2003
Tongue
English
Weight
104 KB
Volume
11
Category
Article
ISSN
1063-8539

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✦ Synopsis

Abstract

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. Β© 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

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