Linear Forms in Finite Sets of Integers |
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Authors: | Han Shu-Ping Kirfel Christoph Nathanson Melvyn B. |
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Affiliation: | (1) Department of Mathematics, CUNY Graduate School, New York, NY, 10036;(2) Department of Mathematics, Bergen College, N-5030 Landås, Bergen, Norway. E-mail;(3) Department of Mathematics, Lehman College (CUNY), Bronx, NY, 10468. E-mail |
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Abstract: | Let A_1, ..., A_r be finite, nonempty sets of integers, and let h_1,..., h_r be positive integers. The linear formh_1A_1 + ··· + h_rA_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 ofh_i elements of the set A_i. In this paper, the structure of the linear form h_1A_1 + ··· + h_rA_r is completely determined for all sufficiently large integersh_i . |
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Keywords: | sums of sets of integers sumsets growth in semigraphs additive number theory |
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