加性数论中的若干问题。有限集合的集合的大小

IF 0.6 3区数学 Q3 MATHEMATICS

Acta Mathematica Hungarica Pub Date : 2025-09-22 DOI:10.1007/s10474-025-01559-7

M. B. Nathanson

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引用次数: 0

摘要

在有限整数集的和的研究中，大多数注意力都集中在小集合（Freiman定理和相关工作）和大集合（Sidon集合和\(B_h\) -集合）上。本文研究了一组\(k\)整数的\(h\) -折叠和的全范围大小。提出了许多新的结果和尚未解决的问题。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Problems in additive number theory. VI: Sizes of sumsets of finite sets

In the study of sums of finite sets of integers, most attention has been paid to sets with small sumsets (Freiman's theorem and related work) and to sets with large sumsets (Sidon sets and \(B_h\)-sets). This paper focuses on the full range of sizes of \(h\)-fold sums of a set of \(k\) integers. Many new results and open problems are presented.

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来源期刊

Acta Mathematica Hungarica 数学-数学

CiteScore

1.50

自引率

11.10%

发文量

审稿时长

4-8 weeks

期刊介绍： Acta Mathematica Hungarica is devoted to publishing research articles of top quality in all areas of pure and applied mathematics as well as in theoretical computer science. The journal is published yearly in three volumes (two issues per volume, in total 6 issues) in both print and electronic formats. Acta Mathematica Hungarica (formerly Acta Mathematica Academiae Scientiarum Hungaricae) was founded in 1950 by the Hungarian Academy of Sciences.