The Hilton–Milner theorem for attenuated spaces

Non-trivial $t$-intersecting families for the distance-regular graphs of bilinear forms

“…In [24,28], the authors proved the Erdős-Ko-Rado Theorem for V n,0 using different methods, and Ou et al [27] generalized this result to V m,k . In [19] and [25], the authors proved the Hilton-Milner Theorem for V n,0 and V m,0 , respectively. In this paper, we consider the structure of maximal non-trivial t-intersecting families of V n,0 with ℓ ≥ n. When t = n − 1, from the structure of maximal (n − 1)-intersecting families of V n or [21, Lemma 17], one can deduces that each maximal (n − 1)-intersecting family of V n,0 is a collection of all (n, 0)-subspaces of V containing some fixed (n − 1, 0)-subspace of V , or a collection of all (n, 0)-subspaces of V contained in some (n + 1, 1)-subspace of V .…”