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

Benjian Lv; Kaishun Wang; Mengyu Cao; Sanming Zhou

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Non-trivial t-intersecting families for vector spaces

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arxiv 2007.11767 v1 pith:WRY5IPTW submitted 2020-07-23 math.CO

Non-trivial t-intersecting families for vector spaces

Mengyu Cao , Benjian Lv , Kaishun Wang , Sanming Zhou This is my paper

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keywords familiesintersectingnon-trivialvectordimensionalsizespacescase

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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.

Non-trivial t-intersecting families for vector spaces

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