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

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

• ISBN13: 9780521283786
• ISBN10: 0521283787
• Format: Paperback
• Copyright: 1981-06-30
• Publisher: Cambridge University Press

Summary

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.

Table of Contents

Introduction

Generalized Steiner systems of type 3-(v, {4, 6}, 1)

Some remarks on D. R. Hughes' construction of M12 and its associated designs

On k-sets of class [0, 1, 2, n]2 in PG(r,q)

Covering graphs and symmetric designs

Flat embeddings of 2n-gons

Codes, caps and linear spaces

Geometries originating from certain distance regular graphs

Transitive automorphism groups of finite quasifields

On k-sets of type (m,n) in projective planes of square order

On k-sets of type (m,n) in a Steiner system S(2, l, c)

Some translation planes of order 81

A new partial geometry constructed from the Hoffman-Singleton graph

Locally cotriangular graphs

Coding theory of designs

On shears in fixed-point-free affine groups

On (k,n) -arcs and the falsity of the Lunelli-Cse conjecture

Cubic surfaces whose points all lie on their 27 lines

Existence results for translation nets

Translation planes having PSL(2,w) or SL(3,w) as a collineation group

Sequenceable groups: a survey

Polar spaces embedded in a projective space

On relations among the projective geometry codes

Partition loops and affine geometries

Regular cliques in graphs and special 1 1/2- designs

Bericht über Hecke Algebren und Coxeter Alegebren endlicher

On buildings and locally finite Tits geometries

Moufand conditions from finite generalized quadrangles

Embedding geometric lattices in a projective space

Coverings of certain finite geometries

On class-regular projective Hjelmslev planes

On multiplicity-free permutation representations

On a characterization of the Grassman manifold representing the lines in a projective space

Affine subplanes of projective planes

Point stable designs

Other talks

Participants

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