MathDB
2017 Combinatorics #9: Good Sets

Source:

February 20, 2017
symmetry

Problem Statement

Let mm be a positive integer, and let TT denote the set of all subsets of {1,2,…,m}\{1, 2, \dots, m\}. Call a subset SS of TT δ\delta-[I]good[/I] if for all s1,s2∈Ss_1, s_2\in S, s1≠s2s_1\neq s_2, ∣Δ(s1,s2)∣≥δm|\Delta (s_1, s_2)|\ge \delta m, where Δ\Delta denotes the symmetric difference (the symmetric difference of two sets is the set of elements that is in exactly one of the two sets). Find the largest possible integer ss such that there exists an integer mm and 10242047 \frac{1024}{2047}-good set of size ss.
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