Algebraic Graph Theory Seminar - Nathan Lindzey

Title: Yet Another Proof of the Erdős-Ko-Rado Theorem

Abstract:

We give a short new algebraic proof of the Erdős-Ko-Rado theorem, that for k < n/2, the largest families of k-sets of an n-element set such that any two of its members intersect are precisely those families composed of all k-sets that contain some fixed element. Time permitting, we discuss how this proof generalizes to other combinatorial domains. Joint work with Yuval Filmus: arXiv:2201.02887.