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; ∞.
ASJC Scopus subject areas
- Theoretical Computer Science
- Statistics and Probability
- Computational Theory and Mathematics
- Applied Mathematics