A CONVEX SET WITH A RICH DIFFERENCE

被引：1

作者：

Roche-Newton, O. ^{[1
]}

Warren, A. ^{[2
]}

机构：

[1] Johannes Kepler Univ Linz, Inst Algebra, Linz, Austria

[2] Johann Radon Inst Computat & Appl Math, Linz, Austria

来源：

ACTA MATHEMATICA HUNGARICA | 2022年 / 168卷 / 02期

基金：

奥地利科学基金会;

关键词：

arithmetic combinatorics; Sidon; construction;

D O I：

10.1007/s10474-022-01286-3

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We construct a convex set A with cardinality 2n and with the property that an element of the difference set A - A can be represented in n different ways. We also show that this construction is optimal by proving that for any convex set A, the maximum possible number of representations an element of A - A can have is left perpendicular vertical bar A vertical bar/2right perpendicular.

引用

页码：587 / 592

页数：6

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