Set-systems with prescribed cardinalities for pairwise intersections

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Abstract

Suppose that A is a finite set-system on N points, and for everytwo different A, A′ε{lunate} A we have |A∩A′|=0 or r. Then we prove that |A≤ ⌊ N r⌋ 2+⌊ N r⌋+(N-r⌊ N r⌋) whenever N>N0(r). The extremal family is unique and consists of 2r, r and 1-elements sets only. The assumption N>N0(r) can not be omitted. We state some further results and problems.

Original languageEnglish
Pages (from-to)53-67
Number of pages15
JournalDiscrete Mathematics
Volume40
Issue number1
DOIs
Publication statusPublished - 1982

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics

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