Finite Geometries and Designs de P. J. Cameron

Finite Geometries and Designs: Proceedings of the Second Isle of Thorns Conference 1980: London Mathematical Society Lecture Note Series, cartea 49

P. J. Cameron

J. W. P. Hirschfeld

D. R. Hughes

en Limba Engleză Paperback – 15 apr 1981

Originally published in 1981, this collection of 33 research papers follows from a conference on the interwoven themes of finite Desarguesian spaces, Steiner systems, coding theory, group theory, block designs, generalized quadrangles, and projective planes. There is a comprehensive introduction, which aims to interest the non-specialist in the subject and which indicates how the contributions fit together. This is a field of research pursued both for its intrinsic interest and its applications. These papers include a number of open problems whose statement requires very little mathematical sophistication.

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Cuprins

Introduction; Generalized Steiner systems of type 3-(v, {4, 6}, 1) E. F. Assmus Jr. and J. E. Novillo Sardi; 2. Some remarks on D. R. Hughes' construction of M12 and its associated designs T. Beth; 3. On k-sets of class [0, 1, 2, n]2 in PG(r,q) A. Bichara; 4. Covering graphs and symmetric designs R. L. Riggs and T. Ito; 5. Flat embeddings of 2n-gons F. J. Cameron; 6. Codes, caps and linear spaces F. V. Coccherini and G. Tallini; 7. Geometries originating from certain distance regular graphs A. M. Cohen; 8. Transitive automorphism groups of finite quasifields S. D. Cohen, M. J. Ganley and V. Jha; 9. On k-sets of type (m,n) in projective planes of square order M. de Finis; 10. On k-sets of type (m,n) in a Steiner system S(2, l, c) M. J. de Resmini; 11. Some translation planes of order 81 D. A. Foulser; 12. A new partial geometry constructed from the Hoffman–Singleton graph W. Haemers; 13. Locally cotriangular graphs J. I. Hall and E. E. Shult; 14. Coding theory of designs M. Hall Jr.; 15. On shears in fixed-point-free affine groups C. Hering; 16. On (k,n) -arcs and the falsity of the Lunelli–Cse conjecture R. Hill and J. R. M. Mason; 17. Cubic surfaces whose points all lie on their 27 lines J. W. P. Hirschfeld; 18. Existence results for translation nets D. Jungnickel; 19. Translation planes having PSL(2,w) or SL(3,w) as a collineation group M. J. Kalleher; 20. Sequenceable groups: a survey A. D. Keedwell; 21. Polar spaces embedded in a projective space Lefèvre-Percsy; 22. On relations among the projective geometry codes R. A. Liebler; 23. Partition loops and affine geometries M. Marchi; 24. Regular cliques in graphs and special 1 1/2- designs A. Neumaier 25. Bericht über Hecke Algebren und Coxeter Alegebren endlicher Geometrien U. Ott; 26. On buildings and locally finite Tits geometries U. Ott and M. A. Ronan; 27. Moufand conditions from finite generalized quadrangles S. E. Payne and J. A. Thas; 28. Embedding geometric lattices in a projective space N. Percsy; 29. Coverings of certain finite geometries M. A. Ronan; 30. On class-regular projective Hjelmslev planes S. S. Sane; 31. On multiplicity-free permutation representations J. Saxl; 32. On a characterization of the Grassman manifold representing the lines in a projective space G. Tallini; 33. Affine subplanes of projective planes K. Vedder; 34. Point stable designs K. E. Wolff; Other talks; Participants.