A new extension of the Erdos-Heilbronn conjecture
Abstract
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.
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