An algebraic groups perspective on Erdős–Ko–Rado

Abstract

We give a proof of the Erdős–Ko–Rado Theorem using the Borel Fixed-Point Theorem from algebraic group theory. This perspective gives a strong analogy between the Erdős–Ko–Rado Theorem and (generalizations of) the Gerstenhaber Theorem on spaces of nilpotent matrices.

Keywords:

• Erdős–Ko–Rado
• exterior algebra
• Borel fixed-point

Acknowledgments

Thanks to Roya Beheshti, Jan Draisma and to Mathematics Stackoverflow user Lazzaro Campeotti [29] for helping me with the algebraic geometry background, particularly with understanding how to define a subvariety of the Grassmannian from a projective variety. Thanks to Claude Roché for pointing out the relevant work of de Rham. Thanks to Alex Scott and Elizabeth Wilmer for discussing the relationship with their work.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported in part by the Slovenian Research Agency (research program P1-0285 and research projects J1-9108, N1-0160, J1-2451, J3-3003).