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- W1734900768 abstract "We view a design D as a set of k-subsets of a fixed set X of v points. A k-subset of X is at distance i from D if it intersects some k-set in D in k − i points, and no subset in more than k − i points. Thus D determines a partition by distance of the k-subsets of X. We say D is completely transitive if the cells of this partition are the orbits of the automorphism group of D in its induced action on the k-subsets of X. This paper initiates a study of completely transitive designs D. A classification is given of all examples for which the automorphism group is not primitive on X. In the primitive case the focus is on examples with the property that any two distinct k-subsets in D have at most k −3 points in common. Here a reduction is given to the case where the automorphism group is 2-transitive on X. New constructions are given by classifying all examples for some famlies of 2-transitive groups, leaving several unresolved cases." @default.
- W1734900768 created "2016-06-24" @default.
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- W1734900768 date "2014-05-09" @default.
- W1734900768 modified "2023-09-27" @default.
- W1734900768 title "Completely Transitive Designs" @default.
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