Number Theory and Combinatorics Seminar: Venkata Raghu Tej Pantangi

  • Date: 10/06/2021
  • Time: 14:30
Lecturer(s):
Venkata Raghu Tej Pantangi, University of Lethbridge
Location: 

University of Lethbridge

Topic: 

EKR Module Property

Description: 

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.

Other Information: 

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/