# 2-cancellative hypergraphs and codes

Research output: Contribution to journalArticle

### 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 language English 159-177 19 Combinatorics Probability and Computing 21 1-2 https://doi.org/10.1017/S0963548311000563 Published - Jan 2012

Hypergraph
Upper bound
Denote
Distinct
Family

### ASJC Scopus subject areas

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

### Cite this

In: Combinatorics Probability and Computing, Vol. 21, No. 1-2, 01.2012, p. 159-177.

Research output: Contribution to journalArticle

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