Distinct distances with lp metrics

被引：0

作者：

Matthews, Polly, Jr.

AlQady, Moaaz ^{[1
]}

Chabot, Riley ^{[2
]}

Dudarov, William ^{[3
]}

Ge, Linus ^{[4
]}

Juvekar, Mandar ^{[4
]}

Kundeti, Srikanth ^{[5
]}

Kundu, Neloy ^{[6
]}

Lu, Kevin ^{[7
]}

Moreno, Yago ^{[8
]}

Peng, Sibo ^{[9
]}

Speas, Samuel ^{[10
]}

Starzycka, Julia ^{[11
]}

Steinthal, Henry ^{[6
]}

Vitko, Anastasiia ^{[12
]}

机构：

[1] Amer Univ Cairo, New Cairo, Egypt

[2] Princeton Univ, Princeton, NJ 08544 USA

[3] Carleton Coll, Northfield, MN 55057 USA

[4] Univ Rochester, Rochester, NY 14627 USA

[5] Rutgers State Univ, New Brunswick, NJ USA

[6] Lafayette Coll, Easton, PA 18042 USA

[7] Georgia Inst Technol, Atlanta, GA 30332 USA

[8] Univ Bristol, Bristol, Avon, England

[9] North Carolina State Univ, Raleigh, NC 27695 USA

[10] Univ Calif Berkeley, Berkeley, CA 94720 USA

[11] Univ Illinois, Chicago, IL 60680 USA

[12] Wesleyan Univ, Middletown, CT 06459 USA

来源：

COMPUTATIONAL GEOMETRY-THEORY AND APPLICATIONS | 2022年 / 100卷

关键词：

Distinct distances; Distance metrics; Geometric incidences; Discrete geometry; SETS; NUMBER;

D O I：

10.1016/j.comgeo.2021.101785

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study Ercles's distinct distances problem under l(p) metrics with integer p. We prove that, for every epsilon > 0 and n points in R-2, there exists a point that spans Omega(n(6/7-epsilon)) distinct distances with the other n - 1 points. This improves upon the previous best bound of Omega(n(4/5)). We also characterize the sets that span an asymptotically minimal number of distinct distances under the l(1) and l(infinity) metrics. (C) 2021 Published by Elsevier B.V.

引用

页数：12

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