The Erdos-Ko-Rado theorem for transitive groups

 A set of permutations $\mathcal{F}$ of a finite transitive group $G\leq \sym(\Omega)$ is \emph{intersecting} if any two permutations in $\mathcal{F}$ agree on an element of $\Omega$. The transitive group $G$ is said to have the \emph{Erd\H{o}s-Ko-Rado (EKR) property} if any intersecting set of $G$ has size at most $\frac{|G|}{|\Omega|}$.

    The alternating group $Alt(4)$ acting on the six $2$-subsets of $\{1,2,3,4\}$ is an example of groups without the EKR property. Hence, transitive groups need not have the EKR property.    Given a transitive group $G\leq \sym(\Omega)$, we are interested in finding the size and structure of the largest intersecting sets in $G$. In this talk, we will give an overview of the EKR-theory for transitive groups and present some recent development in this area.

Join Zoom meeting here: 

https://upr-si.zoom.us/j/86104965231?pwd=SFZoMWFpbTN4SmtCMXc1OVVQQmVEQT09

We are looking forward to meeting at the video conference. 

See you there!