Sharp bounds for sets with distinct subset products

IF 0.6 3区数学 Q3 MATHEMATICS

Acta Mathematica Hungarica Pub Date : 2025-12-25 DOI:10.1007/s10474-025-01578-4

R. Raghavan

引用次数: 0

Abstract

Let \(A\subseteq [N]\) be such that for any pair of distinct subsets \(B,C\subseteq A\), the products \(\prod_{b\in B}b\) and \(\prod_{c\in C}c\) are distinct. We prove that \(|A|\leq \pi(N)+\pi(N^{1/2})+o(\pi(N^{1/2}))\), where \(\pi\) is the prime counting function, answering a question of Erdős.

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具有不同子集积的集合的锐利界

设\(A\subseteq [N]\)对于任意一对不同的子集\(B,C\subseteq A\)，乘积\(\prod_{b\in B}b\)和\(\prod_{c\in C}c\)都是不同的。我们证明了\(|A|\leq \pi(N)+\pi(N^{1/2})+o(\pi(N^{1/2}))\)，其中\(\pi\)是素数计数函数，回答了Erdős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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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.