49 research outputs found
Perfect 2-colorings of the grassmann graph of planes
We construct an infinite family of intriguing sets, or equivalently perfect 2-colorings, that are not tight in the Grassmann graph of planes of PG(n, q), n ≥ 5 odd, and show that the members of the family are the smallest possible examples if n ≥ 9 or q ≥ 25
Sets of generators blocking all generators in finite classical polar spaces
We introduce generator blocking sets of finite classical polar spaces. These
sets are a generalisation of maximal partial spreads. We prove a
characterization of these minimal sets of the polar spaces Q(2n,q), Q-(2n+1,q)
and H(2n,q^2), in terms of cones with vertex a subspace contained in the polar
space and with base a generator blocking set in a polar space of rank 2.Comment: accepted for J. Comb. Theory
Partial ovoids and partial spreads in finite classical polar spaces
We survey the main results on ovoids and spreads, large maximal partial ovoids and large maximal partial spreads, and on small maximal partial ovoids and small maximal partial spreads in classical finite polar spaces. We also discuss the main results on the spectrum problem on maximal partial ovoids and maximal partial spreads in classical finite polar spaces
On the smallest non-trivial tight sets in Hermitian polar spaces
We show that an x-tight set of the Hermitian polar spaces H(4; q(2)) and H(6; q(2)) respectively, is the union of x disjoint generators of the polar space provided that x is small compared to q. For H(4; q(2)) we need the bound x < q + 1 and we can show that this bound is sharp