2-cancellative hypergraphs and codes

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

A family of sets F (and the corresponding family of 0-1 vectors) is called t-cancellative if, for all distinct t + 2 members A 1,⋯, A t and B, C ∈ F, A 1∪⋯∪ A t∪ B ≠ A 1∪ ⋯ ∪ A t ∪ C. Let ct(n) be the size of the largest t-cancellative family on n elements, and let ct(n, r) denote the largest r-uniform family. We improve the previous upper bounds, e.g., we show c 2(n) ≤ 2 0.322n (for n > n 0). Using an algebraic construction we show that c 2(n, 2k) = Θ(n k) for each k when n %rarr; ∞.

Original languageEnglish
Pages (from-to)159-177
Number of pages19
JournalCombinatorics Probability and Computing
Volume21
Issue number1-2
DOIs
Publication statusPublished - Jan 1 2012

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Statistics and Probability
  • Computational Theory and Mathematics
  • Applied Mathematics

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