Non-trivial $t$-intersecting families for vector spaces

Abstract

Let $V$ be an $n$-dimensional vector space over a finite field ${\mathbb{F}}_q$. In this paper we describe the structure of maximal non-trivial $t$-intersecting families of $k$-dimensional subspaces of $V$ with large size. We also determine the non-trivial $t$-intersecting families with maximum size. In the special case when $t=1$ our result gives rise to the well-known Hilton-Milner Theorem for vector spaces.

26 pages

Cited by in corpus (2)

• Hilton-Milner results in projective and affine spaces
• Non-trivial $t$-intersecting families for the distance-regular graphs of bilinear forms