Sets of generators blocking all generators in finite classical polar spaces

Abstract

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.keywords: partial spreads, blocking sets, finite classical polar spaces. MSC 2010: 51E20, 51E21. Affiliations:

Approximately strongly regular graphs

“…Note that 1-systems are rarely known, cf. [14,30,40]. One interesting example in our context is a line spread of O − (6, q) which is a 1-system of O(7, q).…”

“…Planes spreads always exist for Sp(6, q), never exist for O + (5, q) and U (5, q), and otherwise the situation is unclear, cf. [14]. Let Y denote the set of lines which are contained in one element of S. Then the inner distribution of Y is a = (1, q 2 + q, 0, q e+2 (q + 1), q e+4 ).…”

Equivalent definitions for (degree one) Cameron–Liebler classes of generators in finite classical polar spaces

“…Among the classical substructures of polar spaces ovoids are among the most studied. They were introduced in [50] and we refer to [14] for a recent overview. An m-ovoid is a set of points of the polar space such that each generator of the polar space contains precisely m of these points.…”