Abstract
A family of sets(and the corresponding family of 0–1 vectors) is calledt-cancellativeif, for all distinctt+ 2 membersA1,. . .,AtandB,C∈,Letct(n) be the size of the largestt-cancellative family onnelements, and letct(n,r) denote the largestr-uniform family. We improve the previous upper bounds,e.g., we showc2(n) ≤ 20.322n(forn>n0). Using an algebraic construction we show thatc2(n, 2k) = Θ(nk) for eachkwhenn→ ∞.
Publisher
Cambridge University Press (CUP)
Subject
Applied Mathematics,Computational Theory and Mathematics,Statistics and Probability,Theoretical Computer Science
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