Erds-Ko-Rado Theorems

Aimed at graduate students and researchers, this fascinating text provides a comprehensive study of the Erdős-Ko-Rado (EKR) Theorem, with a focus on algebraic methods. The authors begin by discussing well-known proofs of the EKR bound for intersecting families. The natural generalization of the EKR Theorem holds for many different objects that have a notion of intersection, and the bulk of this book focuses on algebraic proofs that can be applied to these different objects. The authors introduce tools commonly used in algebraic graph theory and show how these can be used to prove versions of the EKR Theorem. Topics include association schemes, strongly regular graphs, distance regular graphs, the Johnson scheme, the Hamming scheme, and the Grassmann scheme. The book also gives an introduction to representation theory (aimed at combinatoralists) with a focus on the symmetric group. This theory is applied to orbital schemes, concentrating on the perfect matching scheme and other partitions, and to conjugacy class schemes, with an emphasis on the symmetric group. -- back cover.