On the density of sets of vectors

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Answering a question of Erdös, Sauer [4] and independently Perles and Shelah [5] found the maximal cardinality of a collection F of subsets of a set: N of cardinality n such that for every subset M ⊂ N of cardinality m |{C ∩ M: C ε{lunate} F}| < 2m. Karpovsky and Milman [3] generalised this result. Here we give a short proof of these results and further extensions.

Original languageEnglish (US)
Pages (from-to)199-202
Number of pages4
JournalDiscrete Mathematics
Issue number2
StatePublished - 1983
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics


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