Shadows and intersections in vector spaces

Ameera Chowdhury, Balázs Patkós

Research output: Contribution to journalArticlepeer-review

27 Scopus citations

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 languageEnglish (US)
Pages (from-to)1095-1106
Number of pages12
JournalJournal of Combinatorial Theory. Series A
Volume117
Issue number8
DOIs
StatePublished - Nov 2010

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

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