Dávid Tóth: Intersecting families of polynomials over finite fields

We consider an analog of the Erdős-Ko-Rado theorem: a family of degree n monic polynomials over a finite field is said to be k-intersecting if the greatest common divisor of any two elements of it has degree at least k. For every finite field, we determine all extremal (i.e., maximal size) k-intersecting families of degree n (for every n>k>0). This is joint work with Nika Salia. 

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