## Number Theory and Combinatorics Seminar: Venkata Raghu Tej Pantangi

- Date: 10/06/2021
- Time: 14:30

University of Lethbridge

EKR Module Property

Let *G* be a finite group acting transitively on *X*. We say *g, h* ∈ *G* are intersecting if *gh-1 *fixes a point in *X*. A subset *S* of *G* is said to be an intersecting set if every pair of elements in *S* intersect. Cosets of point stabilizers are canonical examples of intersecting sets. The group action version of the classical Erdos-Ko-Rado problem asks about the size and characterization of intersecting sets of maximum possible size. A group action is said to satisfy the EKR property if the size of every intersecting set is bounded above by the size of a point stabilizer. A group action is said to satisfy the strict-EKR property if every maximum intersecting set is a coset of a point stabilizer. It is an active line of research to find group actions satisfying these properties. It was shown that all 2-transitive satisfy the EKR property. While some 2-transitive groups satisfy the strict-EKR property, not all of them do. However a recent result shows that all 2-transitive groups satisfy the slightly weaker “EKR-module property”(EKRM), that is, the characteristic vector of a maximum intersecting set is a linear span of characteristic vectors of cosets of point stabilizers. We will discuss about a few more infinite classes of group actions that satisfy the EKRM property. I will also provide a few non-examples and a characterization of the EKRM property using characters of *G*.

Event held in-person and online:

In-person Location: SA 6006

Zoom link and password available from the organizers:

Bobby.Miraftab@uleth.ca or Raghu.Pantangi@uleth.ca

If possible, please write from a verifiable university email address, and not at the last minute.

Event page:

https://www.cs.uleth.ca/~nathanng/ntcoseminar/