Cross-Intersecting Erdős-Ko-Rado Sets in Finite Classical Polar Spaces

Abstract

A cross-intersecting Erdős-Ko-Rado set of generators of a finite classical polar space is a pair $(Y,Z)$ of sets of generators such that all $y\in Y$ and $z\in Z$ intersect in at least a point. We provide upper bounds on $|Y|\cdot |Z|$ and classify the cross-intersecting Erdős-Ko-Rado sets of maximum size with respect to $|Y|\cdot |Z|$ for all polar spaces except Hermitian polar spaces in odd projective dimension.