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2-Cancellative Hypergraphs and Codes
Published online by Cambridge University Press: 02 February 2012
Abstract
A family of sets (and the corresponding family of 0–1 vectors) is called t-cancellative if, for all distinct t + 2 members A1,. . ., At and B, 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 c2(n) ≤ 20.322n (for n > n0). Using an algebraic construction we show that c2(n, 2k) = Θ(nk) for each k when n → ∞.
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- Combinatorics, Probability and Computing , Volume 21 , Issue 1-2: Honouring the Memory of Richard H. Schelp , March 2012 , pp. 159 - 177
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- Copyright © Cambridge University Press 2012
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