The Typical Structure of Sets With Small Sumset

被引：1

作者：

Campos, Marcelo ^{[1
]}

Collares, Mauricio ^{[2
]}

Morris, Robert ^{[1
]}

Morrison, Natasha ^{[3
]}

Souza, Victor ^{[1
]}

机构：

[1] IMPA, Estr Dona Castorina 110, BR-22460320 Rio De Janeiro, Brazil

[2] Univ Fed Minas Gerais, Dept Matemat, BR-31270901 Belo Horizonte, MG, Brazil

[3] Univ Victoria, Dept Math & Stat, David Turpin Bldg,3800 Finnerty Rd, Victoria, BC V8P 5C2, Canada

来源：

INTERNATIONAL MATHEMATICS RESEARCH NOTICES | 2022年 / 2022卷 / 14期

关键词：

COUNTING SETS; NUMBER; THEOREM;

D O I：

10.1093/imrn/rnab021

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper we determine the number and typical structure of sets of integers with bounded doubling. In particular, improving recent results of Green and Morris, and of Mazur, we show that the following holds for every fixed lambda > 2 and every k >= (log n)(4): if omega -> infinity as n -> infinity (arbitrarily slowly), then almost all sets A subset of [n] with vertical bar A vertical bar = k and vertical bar A + A vertical bar <= lambda k are contained in an arithmetic progression of length lambda k/2 + omega.

引用

页码：11011 / 11055

页数：45

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