This volume examines state of the art research in finite geometries and designs.
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This volume examines finite geometries and designs, a key area in modern applicable mathematics. It includes state-of-the-art surveys from leading international mathematicians in their fields, and will be a useful reference for researchers in many aspects of combinatorics.
Preface; Introduction; 1. On maximum size anti-Pasch sets of triples; 2. Some simple 7-designs; 3. Inscribed bundles, Veronese surfaces and caps; 4. Embedding partial geometries in Steiner designs; 5. Finite geometry after Aschbacher's theorem: PGL(n,q) from a Kleinian viewpoint; 6. The Hermitian function field arising from a cyclic arc in a Galois plane; 7. Intercalates everywhere; 8. Difference sets: an update; 9. Computational results for the known biplanes of order 9; 10. A survey of small embeddings for partial cycle systems; 11. Rosa triple systems; 12. Searching for spreads and packings; 13. A note of Buekenhout–Metz unitals; 14. Elation generalized quadrangles of order (q^2, q); 15. Uniform parallelisms of PG(3,3); 16. Double-fives and partial spreads in PG(5,2); 17. Rank three geometries with simplicial residues; 18. Generalized quadrangles and the Axiom of Veblen; Talks; Participants.
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