Department of Mathematical Sciences
Discrete Math Seminar
Tuesday, October 7th, 2025
4:00PM-4:50PM
Olin Hall 126
Speaker: Alena Ernst, WPI
Title: An Introduction to the World of Erdős–Ko–Rado Problems
Abstract: Two of the most famous problems in combinatorics are as follows: How large can a family of k-sets of {1,2,…,n} be such that every two members of the family have a non-empty intersection? And what is the characterisation of the families of maximal size?
These are the classical examples of a class of combinatorial problems known as intersecting problems. They are also called Erdős-Ko-Rado (EKR) problems, in honour of the mathematicians who first proposed and solved them. In this talk, we introduce the world of EKR problems: we explore a variety of objects, notions of intersection, and proof techniques.