A new extension of the Erdos-Heilbronn conjecture

الأصل · EN

Let A₁,...,Aₙ be finite subsets of a field F, and let f(x₁,...,xₙ)=x₁ᵏ+...+xₙᵏ+g(x₁,...,xₙ)∈ F[x₁,...,xₙ] with deg g<k. We obtain a lower bound for the cardinality of f(x₁,...,xₙ): x₁∈ A₁,...,xₙ∈ Aₙ, and xᵢ=xⱼ if i=j. The result extends the Erdos-Heilbronn conjecture in a new way.