  Let A_1,...,A_n be finite subsets of a field F, and let
f(x_1,...,x_n)=x_1^k+...+x_n^k+g(x_1,...,x_n)\in F[x_1,...,x_n] with deg g<k.
We obtain a lower bound for the cardinality of {f(x_1,...,x_n): x_1\in
A_1,...,x_n\in A_n, and x_i\not=x_j if i\not=j}. The result extends the
Erdos-Heilbronn conjecture in a new way.
