Counting sets with small sumset
Source: github.com/gdahia/CountingSetsWithSmallSumset/tree/8d89dcad…
Lean 4 formalization of Green's paper Counting sets with small sumset, and the clique number of random Cayley graphs. For a finite abelian group Γ, let S_k^m(Γ) be the family of the sets X in Γ with |X| = k whose restricted sumset X ∔ X = {x + y : x, y in X, x ≠ y} has m elements. The paper bounds |S_k^m(Γ)| for Γ = Z/NZ and Γ = F_2^n, through a bound for the number of Freiman isomorphism classes of sets with small restricted sumset in a vector space. It deduces that the Cayley sum graph of a random subset of Z/NZ almost surely has clique number at most 160 log_2 N, and that the Cayley graph…
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