A characterization of the natural embedding of the split Cayley hexagon H(q) in PG(6, q) by intersection numbers

Abstract:In this paper, we prove that a set L of q(5) + q(4) + q(3) + q(2) + q + 1 lines of PG(6, q) with the properties that (1) every point of PG(6, q) is incident with either 0 or q + I elements of L, (2) every plane of PG(6, q) is incident with either 0, 1 or q + I elements of L, (3) every solid of PG(6, q) is incident with either 0, 1, q + 1 or 2q + 1 elements of L, and (4) every hyperplane of PG(6, q) is incident with at most q(3) + 3q(2) + 3q members of L, is necessarily the set of lines of a regularly embedded split Cayley generalized hexagon H(q) in PG(6, q).

Publication year:2008

Keywords:Pure mathematics