Erdos-Ko-Rado Theorems: Algebraic Approaches

Chris Godsil (University of Waterloo) and Karen Meagher (University of Regina) are pleased to announce the publication of their book Erdös-Ko-Rado Theorems: Algebraic Approaches, Cambridge University Press.

The Erdös-Ko-Rado theorem, a central result in extremal combinatorics, gives a bound on the size of a family of intersecting k-subsets of a set and describes exactly which families meet this bound. The theorem has been extended to many objects other than subsets of a set, including subspaces of a vector space over a finite field, integer sequences, blocks in a design, partitions, and permutations.

The Godsil-Meagher book focuses on algebraic proofs of analogues of the Erdös-Ko-Rado theorem for cocliques, permuations, and partitions. The proofs use standard tools from algebraic graph theory; the book provides an introduction to these tools including association schemes, strongly regular graphs, the Johnson scheme, the Hamming scheme, and the Grassmann scheme.

The book includes 170 end-of-chapter exercises and concludes with 15 open problems.