This volume contains nine survey articles which provide expanded accounts of plenary seminars given at the British Combinatorial Conference at the University of Strathclyde in July 2017. This biennial conference is a well-established international event attracting speakers from around the world. Written by internationally recognised experts in the field, these articles represent a timely snapshot of the state of the art in the different areas of combinatorics. Topics covered include the robustness of graph properties, the spt-function of Andrews, switching techniques for edge decompositions of graphs, monotone cellular automata, and applications of relative entropy in additive combinatorics. The book will be useful to researchers and advanced graduate students, primarily in mathematics but also in computer science and statistics.

• Provides nine survey articles by world-leading researchers in combinatorics • Summarises the current state of the field • Accessible to non-experts

### Contents

1. Relations among partitions R. A. Bailey; 2. Large-scale structures in random graphs Julia Böttcher; 3. The spt-function of Andrews William Y. C. Chen; 4. Combinatorial structures in finite classical polar spaces Antonio Cossidente; 5. Switching techniques for edge decompositions of graphs Daniel Horsley; 6. Ramsey-type and amalgamation-type properties of permutations Vít Jelínek; 7. Monotone cellular automata Robert Morris; 8. Robustness of graph properties Benny Sudakov; 9. Some applications of relative entropy in additive combinatorics Julia Wolf.