a Department of Mathematics, University of California San Diego, La Jolla, CA, 92093, USA b Department of Computer Science, The University of Memphis, Memphis, TN, 38152, USA
Abstract:
We prove a vector space analog of a version of the Kruskal-Katona theorem due to Lovász. 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?s-Ko-Rado theorem for vector spaces.