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 Erdo{double acute}s-Ko-Rado theorem for vector spaces.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 1095-1106 |
| Number of pages | 12 |
| Journal | Journal of Combinatorial Theory. Series A |
| Volume | 117 |
| Issue number | 8 |
| DOIs | |
| State | Published - Nov 2010 |
| Externally published | Yes |
Bibliographical note
Funding Information:E-mail addresses: anchowdh@math.ucsd.edu (A. Chowdhury), bpatkos@memphis.edu (B. Patkós). 1 Supported by NSF Grant #: CCF-0728928.
Funding Information:
The first author thanks the NSF for supporting her and the Rényi Institute for hosting her while she was an NSF-CESRI fellow during the summer of 2008. We also thank Jacques Verstraëte for carefully reading this manuscript.
Keywords
- Erdo{double acute}s-Ko-Rado
- Intersecting family
- Kruskal-Katona
- Shadow
- Vector space