On sum sets of sets having small product set
نویسندگان
چکیده
منابع مشابه
Zero-sum free sets with small sum-set
Let A be a zero-sum free subset of Zn with |A| = k. We compute for k ≤ 7 the least possible size of the set of all subset-sums of A.
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Let A and B be two finite sets of numbers. The sum set and the product set of A,B are A+B : = {a+b : a ∈ A, b ∈ B}, and AB : = {ab : a ∈ A, b ∈ B}. We prove that A + B is as large as possible when AA is not too big. Similarly, AB is large when A + A is not too big. The methods rely on the λp constant of A, bound on the number of factorizations in a generalized progression containing A, and the ...
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ژورنال
عنوان ژورنال: Proceedings of the Steklov Institute of Mathematics
سال: 2015
ISSN: 0081-5438,1531-8605
DOI: 10.1134/s0081543815060255