Finite Geometries and Designs: Proceedings of the Second Isle of Thorns Conference 1980

by P. J. Cameron, J. W. P. Hirschfeld, D. R. Hughes

Overview

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.

Product Details

ISBN-13:	9780521283786
Publisher:	Cambridge University Press
Publication date:	04/16/1981
Series:	London Mathematical Society Lecture Note Series , #49
Pages:	380
Product dimensions:	5.98(w) x 9.02(h) x 0.87(d)

Table of Contents

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.