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

共 50 条

[31] THE CONVEX HULL OF A BOREL SET
KLEE, VL
[J]. BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY, 1949, 55 (01) : 44 - 44
[32] CLOSURE OF CONVEX HULL OF A SET
LIN, CS
[J]. CANADIAN MATHEMATICAL BULLETIN-BULLETIN CANADIEN DE MATHEMATIQUES, 1975, 18 (01): : 147 - 148
[33] On the stability of a convex set of matrices
Dzhafarov, V
Büyükköroglu, T
[J]. LINEAR ALGEBRA AND ITS APPLICATIONS, 2006, 414 (2-3) : 547 - 559
[34] On the symmetry function of a convex set
Belloni, Alexandre
Freund, Robert M.
[J]. MATHEMATICAL PROGRAMMING, 2008, 111 (1-2) : 57 - 93
[35] On the estimation of a convex set with corners
Hall, P
Turlach, BA
[J]. IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE, 1999, 21 (03) : 225 - 234
[36] RANDOM DIVISIONS OF A CONVEX SET
JANSON, S
[J]. JOURNAL OF APPLIED PROBABILITY, 1978, 15 (03) : 645 - 649
[37] ON THE CONVEX LAYERS OF A PLANAR SET
CHAZELLE, B
[J]. IEEE TRANSACTIONS ON INFORMATION THEORY, 1985, 31 (04) : 509 - 517
[38] Centre of a compact convex set
Karn, Anil Kumar
[J]. BANACH JOURNAL OF MATHEMATICAL ANALYSIS, 2022, 16 (04)
[39] On the symmetry function of a convex set
Alexandre Belloni
Robert M. Freund
[J]. Mathematical Programming, 2008, 111 : 57 - 93
[40] PART METRIC IN A CONVEX SET
BAUER, H
BEAR, HS
[J]. NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY, 1969, 16 (01): : 260 - &

← 1 2 3 4 5 →