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Linear Forms in Finite Sets of Integers (1998)

Han, Shu-Ping ; Kirfel, Christoph ; Nathanson, Melvyn B.

Springer

The Ramanujan journal 2 (1998), S. 271-281

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ISSN: 1572-9303

Keywords: sums of sets of integers ; sumsets ; growth in semigraphs ; additive number theory

Source: Springer Online Journal Archives 1860-2000

Topics: Mathematics

Notes: 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 .

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1023/A:1009734613675

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