Year: 2026
Type: preprint
Abstract: A family of $k$-subspaces of an $n$-dimensional vector space over a finite field is $t$-intersecting if any two members intersect in a subspace of dimension at least $t$. A $t$-intersecting family is nontrivial if no $t$-subspace is contained in all its members. In this paper, we determine the largest nontrivial $t$-intersecting families for $k\geq t+2$ and $n\geq 2k+1$. As a result, the complete nontrivial-intersection theorem for vector spaces is established.
Source: arXiv (Cornell University)
Authors: Liu, Dehai, Lv, Benjian, Wang, Kaishun, Wen, Jie
Institution: Beijing Normal University
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Awards: G2217122181, G302072269, G7840208982
OpenAlex ID: W7220718953