Computational and Constructive Design Theory

Over the last several years, there has been a significant increase in compu­ tational combinatorics. The most widely reported results were, of course, the proof of the Four Color Theorem and the proof that there is no projective plane of parameter 10. Although the computer was essential in both proofs, the only reason for this was the fact that life is short. The computations involved were not different in kind from those which have been done by human brains without electronic assistance; they were just longer. Another important fact to notice is that both problems were theoretical, pure­ mathematical ones. The pursuit of the Four-Color Theorem has led to the development of whole branches of graph theory. The plane of parameter 10 is not an isolated case; its nonexistence is the first (and so far, the only) coun­ terexample to the conjecture that the Bruck-Chowla-Ryser conditions were necessary and sufficient for the existence of a symmetric balanced incomplete block design; the study of this problem has also led to a number of theoretical advances, including investigation of the relationship between codes and designs. Front Matter....Pages i-xiv A Bridge Club Design....Pages 1-12 The First Time....Pages 13-28 Computational Methods in Design Theory....Pages 29-48 Finding Designs with Genetic Algorithms....Pages 49-65 Making the Mols Table....Pages 67-134 On Writing Isomorphism Programs....Pages 135-175 The Nonexistence of 4-(12,6,6) Designs....Pages 177-188 BIBDs with κ = 6 and λ = 1....Pages 189-226 Polyhedral Methods in Design Theory....Pages 227-254 Another Look at Large Sets of Steiner Triple Systems....Pages 255-335 (22, 33, 12, 8, 4)-BIBD, an Update....Pages 337-357 Back Matter....Pages 359-362 This volume is a sequel to the 1996 compilation, Computational and Constructive Design Theory. It contains research papers and surveys of recent research work on two closely related aspects of the study of combinatorial designs: design construction and computer-aided study of designs. Audience: This volume is suitable for researchers in the theory of combinatorial designs The volume contains eleven papers on various computational techniques used in constructive design theory, written by experts in the field. Included are papers on the use of optimization and numerical analysis techniques, construction of classes of combinatorial design, and attempts to block designs with given small parameters. The volume contains two tutorial papers