Discrete Math Seminar: Gabriel Currier

The classical Erdos-Ko-Rado theorem in extremal combinatorics states the following: Given a family F of k-subsets of an n-set that is "pairwise intersecting" (meaning A \cap B \neq \emptyset for all A,B in F) it follows that F can be no larger than \binom{n-1}{k-1}. A commonly-studied extension is whether the same bound can be applied to F if any d elements of F obey some given intersectional structure, for d greater than 2. We will discuss the history of these problems as well as new results on some long-open conjectures.