关于Freiman的3k−4定理

Uniform distribution theory Pub Date : 2019-12-01 DOI:10.2478/udt-2019-0013

M. Huicochea

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引用次数: 2

摘要

设X和Y为𝕑的非空有限子集，X +Y为其集合。当r(X, Y):= |X +Y |−|X|−|Y |较小时，X和Y的结构已被广泛研究;特别地，广义Freiman的3k−4定理描述了当r(X, Y)≤min{|X|， |Y |}−4时的X和Y。然而，当r(X, Y) > min{|X|， |Y |}−4时，对X和Y的了解并不多。本文研究了任意r(X, Y)的X和Y的结构。

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On Freiman’s 3k − 4 Theorem

Abstract Let X and Y be nonempty finite subsets of 𝕑 and X +Y its sumset. The structures of X and Y when r(X, Y ):= |X +Y |−|X|−|Y | is small have been widely studied; in particular the Generalized Freiman’s 3k − 4 Theorem describes X and Y when r(X, Y ) ≤ min{|X|, |Y |} − 4. However, not too much is known about X and Y when r(X, Y ) > min{|X|, |Y |} − 4. In this paper we study the structure of X and Y for arbitrary r(X, Y ).

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Uniform distribution theory

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