Strict EKR robustness of PGL(2,q)

Prove that PGL(2,q) in its natural 2-transitive action is strict EKR robust.

Background

The paper proves ordinary EKR robustness for PGL(2,q) in its natural action, showing that deleting fewer than d_G labels does not increase the independence number. It conjectures the stronger strict EKR robustness property, which would require the star-sized independence number to persist unless a full pair of point-mapping derangement classes has been deleted.

References

It is open if there are other, more interesting, group actions that are strict EKR robust. However, we will make the following conjecture.

Conjecture 7.8. The group PGL(2, q) with its natural 2-transitive action is strict EKR robust.

— A new measure of robustness of Erdős--Ko--Rado Theorems on permutation groups  (2502.14582 - Gunderson et al., 20 Feb 2025) in Conjecture 7.8, Section 7

Conjecture 7.8. The group PGL(2, q) with its natural 2-transitive action is strict EKR robust.

— A new measure of robustness of Erdős--Ko--Rado Theorems on permutation groups  (2502.14582 - Gunderson et al., 20 Feb 2025) in Conjecture 7.8, Section 7