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

2021/03/20 by Mengyu Cao, Cao, Mengyu, Benjian Lv +3
Mathematics · #05A30 #05D05 #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #Graph theory and applications #Limits and Structures in Graph Theory

paper · pdf · doi:10.48550/arxiv.2103.11117

openalex publication_date 2021/03/20 · openalex created_date 2021/03/29 · openalex updated_date 2026/07/28

Abstract

Let V be an (n+ℓ)-dimensional vector space over a finite field, and W a fixed ℓ-dimensional subspace of V. Write V\brack n,0 to be the set of all n-dimensional subspaces U of V satisfying dim(U∩ W)=0. A family F⊆V\brack n,0 is t-intersecting if dim(A∩ B)≥ t for all A,B\inF. A t-intersecting family F⊆V\brack n,0 is called non-trivial if dim(∩_F\inFF)

Citations

• Hilton-Milner results in projective and affine spaces
• The structure of large non-trivial t-intersecting families for finite sets

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• Simplices in t-intersecting families for vector spaces
• Non-trivial t-intersecting families for vector spaces
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• More on r-cross t-intersecting families for vector spaces