{"id":"palomar/PALOMAR-2026-11-03-000013","url":"https://github.com/gdahia/CountingSetsWithSmallSumset/tree/8d89dcad03b9b4e5f50336300c9bee4dcfc2cff2","json":"https://data.palomar-registry.org/entries/PALOMAR-2026-11-03-000013-v1.json","repo":"https://github.com/gdahia/CountingSetsWithSmallSumset","tags":["math.CO","math.NT","msc:11P70","msc:11B13","msc:11B30","msc:05C80","msc:05C55"],"score":0,"title":"Counting sets with small sumset","trust":"high","domain":"math.CO","source":"palomar","authors":["Gabriel Dahia"],"reviews":0,"subject":"math.CO","summary":"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…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"verified":true,"discussed":0,"published":"2026-11-03","reactions":{},"formalized":true,"formalizes":[{"title":"Counting sets with small sumset, and the clique number of random Cayley graphs","identifier":"https://arxiv.org/abs/math/0304183v2","relationship":"formalizes"}]}