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On the structure of the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>h</mml:mi></mml:math>-fold sumsets

On the structure of the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>h</mml:mi></mml:math>-fold sumsets

Let A be a set of nonnegative integers. Let (hA) (t) be the set of all integers in the sumset hA that have at least t representations as a sum of h elements of A. In this paper, we prove that, if k≥2, and A=a 0 ,a 1 ,⋯,a k …