Joseph A. Thas - Böcker

This is a graduate-level book aimed at experienced researchers as well as beginning graduate students in finite geometry, incidence geometry, design theory, coding theory and combinatorics. The 21 articles arise from the Fourth Isle of Thorns Conference on Finite Geometries, held in July 2000. The book contains new high-level results at the forefront of the field as well as authoritative surveys. The articles are written so that beginning graduate students can appreciate them. Among the surveys by the invited speakers are P.J. Cameron ("Fixed Points and cycles"), C.E. Praeger ("Implications of line-transitivity for designs"), B. Schmidt, ("Exponent bounds", which explains recent results on difference sets), and several papers with H. Van Maideghem as co-author on generalized polygons. The editors also contribute: A. Blokhuis, D. Jungnickel, and B. Schmidt ("On a class of symmetric divisible designs which are almost projective planes"), and D. Luyckx and J.A. Thas discuss the geometry of the quadric in six dimensions. There is also a lengthy and complete survey by J.W.P. Hirschfeld and L.Storme ("The packing problem in statistics, coding theory and finite projective spaces: update 2001"). Researchers as well as beginning graduate students in the areas of finite geometry, incidence geometry, design theory, coding theory and combinatorics should appreciate the surveys and original papers by leaders in these fields.

This book is the second edition of the third and last volume of a treatise on projective spaces over a finite field, also known as Galois geometries. This volume completes the trilogy comprised of plane case (first volume) and three dimensions (second volume). This revised edition includes much updating and new material. It is a mostly self-contained study of classical varieties over a finite field, related incidence structures and particular point sets in finite n-dimensional projective spaces. General Galois Geometries is suitable for PhD students and researchers in combinatorics and geometry. The separate chapters can be used for courses at postgraduate level.

This book is the second edition of the third and last volume of a treatise on projective spaces over a finite field, also known as Galois geometries. This volume completes the trilogy comprised of plane case (first volume) and three dimensions (second volume).

When? These are the proceedings of Finite Geometries, the Fourth Isle of Thorns Conference, which took place from Sunday 16 to Friday 21 July, 2000. It was organised by the editors of this volume. The Third Conference in 1990 was published as Advances in Finite Geometries and Designs by Oxford University Press and the Second Conference in 1980 was published as Finite Geometries and Designs by Cambridge University Press. The main speakers were A. R. Calderbank, P. J. Cameron, C. E. Praeger, B. Schmidt, H. Van Maldeghem. There were 64 participants and 42 contributions, all listed at the end of the volume. Conference web site http://www. maths. susx. ac. uk/Staff/JWPH/ Why? This collection of 21 articles describes the latest research and current state of the art in the following inter-linked areas: • combinatorial structures in finite projective and affine spaces, also known as Galois geometries, in which combinatorial objects such as blocking sets, spreads and partial spreads, ovoids, arcs and caps, as well as curves and hypersurfaces, are all of interest; • geometric and algebraic coding theory; • finite groups and incidence geometries, as in polar spaces, gener­ alized polygons and diagram geometries; • algebraic and geometric design theory, in particular designs which have interesting symmetric properties and difference sets, which play an important role, because of their close connections to both Galois geometry and coding theory.