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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/
We are looking forward to meeting at the video conference.
See you there!
Let $\Omega$ be a finite set and $G$ be a permutation group on it.
A subset $A$ of $G$ is \textit{intersecting} if for every $\delta,~\tau \in A$, they agree at some points, i.e. there exists $x \in \Omega$ such that $\delta(x)=\tau(x)$.
In this talk, I will give an analog of the classical Erd\H{o}s–Ko–Rado theorem for intersecting sets of a group. I will present a history and overview of some of the results that have been proved on this subject. Finally, I will discuss some of my results about intersecting sets of the general linear group and its subgroups.
Join Zoom meeting here:
https://upr-si.zoom.us/j/
