Evans, David

English

David M. Evans

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Block transitive Steiner systems with more than one point orbit

For all ‘reasonable’ finite t, k and s we construct a t-(ℵ0, 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-(ℵ0, 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

University of East Anglia digital repository

https://ueaeprints.uea.ac.uk/20042/1/steiner.pdf

Block transitive Steiner systems with more than one point orbit

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University of East Anglia digital repository