Abstract
Let A 1,..., A r be finite, nonempty sets of integers, and let h 1,..., h r be positive integers. The linear form h 1 A 1 +...+ h r A r is the set of all integers of the form b 1+...+b r , where b i is an integer that can be represented as the sum of h i elements of the set A,. In this paper, the structure of the linear form h 1 A 1+...+h r A r is completely determined for all sufficiently large integers h i .Key words:sums of sets of integerssumsetsgrowth in semigraphsadditive number theory1991 Mathematics Subject Classification:Primary 11B05Secondary 11B1311B7511P99
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