Block transitive Steiner systems with more than one point orbit | Zendy

Evans David M. | Zendy

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Block transitive Steiner systems with more than one point orbit

Author(s) -

Evans David M.

Publication year - 2004

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.20018

Subject(s) - automorphism , mathematics , transitive relation , block (permutation group theory) , combinatorics , steiner system , group (periodic table) , orbit (dynamics) , automorphism group , point (geometry) , product (mathematics) , discrete mathematics , geometry , physics , quantum mechanics , engineering , aerospace engineering

For all ‘reasonable’ finite t , k , and s , we construct a t ‐(ℵ 0 , k , 1) design and a group of automorphisms which is transitive on blocks and has s orbits on points. In particular, there is a 2‐(ℵ 0 , 4, 1) design with a block‐transitive group of automorphisms having two point orbits. This answers a question of P. J. Cameron and C. E. Praeger. The construction is presented in a purely combinatorial way, but is a by‐product of a new way of looking at a model‐theoretic construction of E. Hrushovski. © 2004 Wiley Periodicals, Inc.

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