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Homogeneous and ultrahomogeneous Steiner systems
Author(s) -
Devillers Alice
Publication year - 2003
Publication title -
journal of combinatorial designs
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.618
H-Index - 34
eISSN - 1520-6610
pISSN - 1063-8539
DOI - 10.1002/jcd.10034
Subject(s) - isomorphism (crystallography) , mathematics , homogeneous , steiner system , combinatorics , automorphism , automorphism group , discrete mathematics , crystallography , chemistry , crystal structure
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