Surveys in Combinatorics 2013

This volume contains nine survey articles based on the invited lectures given at the 24th British Combinatorial Conference, held at Royal Holloway, University of London in July 2013. This biennial conference is a well-established international event, with speakers from around the world. The volume provides an up-to-date overview of current research in several areas of combinatorics, including graph theory, matroid theory and automatic counting, as well as connections to coding theory and Bent functions. Each article is clearly written and assumes little prior knowledge on the part of the reader. The authors are some of the world's foremost researchers in their fields, and here they summarise existing results and give a unique preview of cutting-edge developments. The book provides a valuable survey of the present state of knowledge in combinatorics, and will be useful to researchers and advanced graduate students, primarily in mathematics but also in computer science and statistics.Preface; 1. Graph removal lemmas David Conlon and Jacob Fox; 2. The geometry of covering codes: small complete caps and saturating sets in Galois spaces Massimo Giulietti; 3. Bent functions and their connections to combinatorics Tor Helleseth and Alexander Kholosha; 4. The complexity of change Jan van den Heuvel; 5. How symmetric can maps on surfaces be? Jozef Siran; 6. Some open problems on permutation patterns Einar Steingrimsson; 7. The world of hereditary graph classes viewed through Truemper configurations Kristina Vuskovic; 8. Structure in minor-closed classes of matroids Jim Geelen, Bert Gerards and Geoff Whittle; 9. Automatic counting of tilings of skinny plane regions Shalosh B. Ekhad and Doron Zeilberger.