For any basis S of R^n, if S+S ⊆ A+B and |A| ≤ n-t then |B| ≥ n + binom(t+1,2), sharp for every S and t.
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A solution to a strengthened conjecture of Bukh, van Hintum and Keevash on additive bases
For any basis S of R^n, if S+S ⊆ A+B and |A| ≤ n-t then |B| ≥ n + binom(t+1,2), sharp for every S and t.