Lectures on Advances in Combinatorics

Rudolf Ahlswede, Professor emeritus of Bielefeld University, has been engaged in research projects to advance a "General Theory of Information Transfer" since his retirement in 2003. He is one of the leading experts in combinatorics, number theory and information theory and has been awarded international prizes and honours, for instance a Honorary Doctorate of the Russian Academy of Sciences in 2001, the Humboldt-Japan Society Senior Scientist Award 1998/99, a Paul Erdos Monetary Award (with Levon Khachatrian) in 1996, the Claude-Elwood-Shannon-Award 2006 of the IEEE Information Theory Society. Since 2004 he has been a member of the European Academy of Sciences. Vladimir Blinovsky has been based at the Institute for Information Transmission Problems of the Russian Academy of Sciences, Moscow since 1981. His scientific interests include combinatorics, coding theory, probability theory, large deviations, and information theory, subjects he has taught in Russia, France, the USA, and Germany.

From the reviews: "The book has some very useful auxiliary material for researchers, namely the open problems at the end of each chapter, and the Appendix at the end of the book. ... there are exercises at the end of each chapter as well. ... the book will be very useful for researchers, and it could serve as the basis of graduate seminar, where each participant presents the material of one lecture covered in this book." (Miklos Bona, MAA Online, January, 2009) "The present book concentrates on special topics in Combinatorial theory. ... At the end of each chapter are exercises, open research problems, and conjectures. More additional material including applications and possible research programs can be found in the Appendix. ... The book can be used as a study material for an advanced graduate course on Combinatorial Theory." (Ludovit Niepel, Zentralblatt MATH, Vol. 1182, 2010)

• Conventions and Auxiliary Results.- Intersection and Diametric Problems.- Covering, Packing, and List Codes.- Higher Level and Dimension Constrained Extremal Problems.- LYM-Related AZ-Identities, Antichain Splittings and Correlation Inequalities.- Basic Problems from Combinatorial Number Theory.