Inverse Theorems for Subset Sums
نویسنده
چکیده
Let A be a nite set of integers. For h 1, let S h (A) denote the set of all sums of h distinct elements of A. Let S(A) denote the set of all nonempty sums of distinct elements of A. The direct problem for subset sums is to nd lower bounds for jS h (A)j and jS(A)j in terms of jAj. The inverse problem for subset sums is to determine the structure of the extremal sets A of integers for which jS h (A)j and jS(A)j are minimal. In this paper both the direct and the inverse problem for subset sums are solved.
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