2-Cancellative Hypergraphs and Codes
Zoltán Füredi · Combinatorics Probability Computing · 2012
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→ ∞.