Erd˝ os-Ko-Rado sets in finite classical polar spaces are sets of generators that intersect pairwise non-trivially. We improve the known upper bound for Erd˝ os-Ko-Rado sets in H(2d + 1, q 2) for d > 2 and d even from approximately q d 2 +d to q d 2 +1 .
A cross-intersecting Erd˝ os-Ko-Rado set of generators of a finite classical polar space is a pair (Y, Z) of sets of generators such that all y ∈ Y and z ∈ Z intersect in at least a point. We provide upper bounds on |Y | · |Z| and classify the cross-intersecting Erd˝ os-Ko-Rado sets of maximum size with respect to |Y | · |Z| for all polar spaces except some… (More)
We develop a theory for ovoids and tight sets in finite classical polar spaces, and we illustrate the usefulness of the theory by providing new proofs for the non-existence of ovoids of particular finite classical polar spaces, including Q + (9, q), q even, and H(5, 4). We also improve the results of A. Klein on the non-existence of ovoids of H(2n + 1, q 2)… (More)