The sumset phenomenon
نویسندگان
چکیده
منابع مشابه
The Sumset Phenomenon
Answering a problem posed by Keisler and Leth, we prove a theorem in nonstandard analysis to reveal a phenomenon about sumsets, which says that if two sets A and B are large in terms of \measure", then the sum A+B is not small in terms of \order{topology". The theorem has several corollaries about sumset phenomenon in the standard world; these are described in sections 2{4. One of these is a ne...
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We prove a generalization of the main theorem in [4] about the sumset phenomenon in the setting of an abelian group with layered tiles of cell measures. Then we give some applications of the theorem for multi–dimensional cases of the sumset phenomenon. Several examples are given in order to show that the applications obtained are not vacuous and cannot be improved in various directions. We also...
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Let G = (G,+) be an additive group. The sumset theory of Plünnecke and Ruzsa gives several relations between the size of sumsets A + B of finite sets A, B, and related objects such as iterated sumsets kA and difference sets A−B, while the inverse sumset theory of Freiman, Ruzsa, and others characterises those finite sets A for which A+A is small. In this paper we establish analogous results in ...
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Let A and B be additive sets of Z2k, where A has cardinality k and B = v.{A with v ∈ Z× 2k. In this note some bounds for the cardinality of A + B are obtained, using four different approaches. We also prove that in a special case the bound is not sharp and we can recover the whole group as a sumset.
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 2001
ISSN: 0002-9939,1088-6826
DOI: 10.1090/s0002-9939-01-06088-9