Quasi-symmetric Designs [Paperback]

The authors discuss comprehensively the generalization of results and applications to quasi-symmetric designs.The authors stress the interaction among designs, finite geometries, and strongly regular graphs in the first study of the theory of quasi-symmetric designs or combinatorial designs with at most two block intersection numbers.The authors stress the interaction among designs, finite geometries, and strongly regular graphs in the first study of the theory of quasi-symmetric designs or combinatorial designs with at most two block intersection numbers.This is the first exposition of the theory of quasi-symmetric designs, that is, combinatorial designs with at most two block intersection numbers. The authors aim to bring out the interaction among designs, finite geometries, and strongly regular graphs. The book starts with basic, classical material on designs and strongly regular graphs and continues with a discussion of some important results on quasi-symmetric designs. The later chapters include a combinatorial construction of the Witt designs from the projective plane of order four, recent results dealing with a structural study of designs resulting from Cameron's classification theory on extensions of symmetric designs, and results on the classification problem of quasi-symmetric designs. The final chapter presents connections to coding theory.Preface; 1. Basic results from designs; 2. Strongly regular graphs and partial geometries; 3. Basic results on quasi-symmetric designs; 4. Some configurations related to strongly regular graphs and quasi-symmetric designs; 5. Strongly regular graphs with strongly regular decompositions; 6. The Witt designs; 7. Extensions of symmetric designs; 8. Quasi-symmetric 2-designs; 9. Towards a classifications of quasi-symmetric 3-designs; 10. Codes and quasi-symmetric designs; References; Index. ...researchers in design theory should find this monograph to be a valuable resource. A.R. Calderbank, Bulletin of the Ameril£Q