# Tutte seminar - Karen Meagher

Friday, June 27, 2014 — 4:00 PM EDT

## The Erdos-Ko-Rado Theorem, An Algebraic Perspective

Speaker: Karen Meagher University of Regina Mike & Ophelia Lazaridis Quantum-Nano Centre (QNC) 0101

### Abstract:

Several years ago I had the good fortune to have an extremely
productive post-doctoral fellowship with Chris. Our work from this
period has culminated in a book about the Erdos-Ko-Rado Theorem (that is $\epsilon$ away from completion!)

This theorem is a major result in extremal set theory. It gives the
exact size and structure of the largest system of sets, with a fixed
number of elements, that has the property that any two sets in the
system have at least one element in common. There are many extensions
of this theorem to combinatorial objects other than set systems, such
as vectors subspaces over a finite field, integer sequences,
partitions, and recently, there have been several results that extend
the EKR theorem to permutations.

During my post-doc with Chris, we worked on an algebraic approach to
proving the EKR theorem for several types of combinatorial
objects. This method is the focus of our book and will be the focus of
my talk. I will explain this method by showing how it can be used to
prove that the natural extension of the EKR theorem holds for
the symmetric group.

Location
QNC - Quantum Nano Centre
0101
200 University Avenue West

Waterloo, ON N2L 3G1

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