Shadows and intersections in vector spaces

We prove a vector space analog of a version of the Kruskal-Katona theorem due to Lov´asz. We apply this result to extend Frankl’s theorem on r-wise intersecting families to vector spaces. In particular, we obtain a short new proof of the Erd˝osKo-Rado theorem for vector spaces.

• Type: Journal
• Year: 2010
• Where: JCT
• Authors: Ameera Chowdhury, Balázs Patkós
• Keywords: JCT 2010, R-wise Intersecting Families, Vector Space Analog, Vector Spaces