Extremal cross t-intersecting families under t-covering number constraints for vector spaces

2026/08/01 by Yu Zhu, Benjian Lv, Kaishun Wang
Mathematics · #math.CO

paper · pdf

arxiv created 2026/08/01 · arxiv updated 2026/08/04

Abstract

Let V be an n-dimensional vector space over the finite field \mathbbF_q, and V\brack k denote the family of all k-dimensional subspaces of V. The families F⊆ V\brack k and G⊆ V\brack ℓ are said to be cross t-intersecting if dim(F∩ G)≥ t for all F\inF and G∈ G. In this paper, we determine the extremal structures when |F||G| attains the maximum value under the conditions dim(∩_{F∈ F}F)<t and dim(∩_{G∈ G}G)<t.

Citations

• A semidefinite programming approach to cross 2-intersecting families
• On a conjecture of Tokushige for cross-t-intersecting families
• More on r-cross t-intersecting families for vector spaces
• A Product Version of the Hilton-Milner-Frankl Theorem
• r-cross t-intersecting families for vector spaces
• The maximum product of weights of cross-intersecting families