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

  • Ferdinand Ihringer
Keywords: Erdős-Ko-Rado Theorem, Polar Space, Association Scheme, Cross-intersecting Family


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 some Hermitian polar spaces.
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