Equilateral sets in lpn

Noga Alon; Pavel Pudlák

doi:10.1007/s00039-003-0418-7

Equilateral sets in l_pⁿ

Noga Alon, Pavel Pudlák

Research output: Contribution to journal › Article › peer-review

20 Scopus citations

Abstract

We show that for every odd integer p ≥ 1 there is an absolute positive constant c_p, so that the maximum cardinality of a set of vectors in Rⁿ such that the l_p distance between any pair is precisely 1, is at most c_pn log n. We prove some upper bounds for other l_p norms as well.

Original language	English (US)
Pages (from-to)	467-482
Number of pages	16
Journal	Geometric and Functional Analysis
Volume	13
Issue number	3
DOIs	https://doi.org/10.1007/s00039-003-0418-7
State	Published - Sep 8 2003
Externally published	Yes

All Science Journal Classification (ASJC) codes

Analysis
Geometry and Topology

Access to Document

10.1007/s00039-003-0418-7

Fingerprint Dive into the research topics of 'Equilateral sets in l<sub>p</sub><sup>n</sup>'. Together they form a unique fingerprint.

Cite this

@article{6129a0ddc46e4d419cc35370657a5751,

title = "Equilateral sets in lpn",

abstract = "We show that for every odd integer p ≥ 1 there is an absolute positive constant cp, so that the maximum cardinality of a set of vectors in Rn such that the lp distance between any pair is precisely 1, is at most cpn log n. We prove some upper bounds for other lp norms as well.",

author = "Noga Alon and Pavel Pudl{\'a}k",

year = "2003",

month = sep,

day = "8",

doi = "10.1007/s00039-003-0418-7",

language = "English (US)",

volume = "13",

pages = "467--482",

journal = "Geometric and Functional Analysis",

issn = "1016-443X",

publisher = "Birkhauser Verlag Basel",

number = "3",

}

TY - JOUR

T1 - Equilateral sets in lpn

AU - Alon, Noga

AU - Pudlák, Pavel

PY - 2003/9/8

Y1 - 2003/9/8

N2 - We show that for every odd integer p ≥ 1 there is an absolute positive constant cp, so that the maximum cardinality of a set of vectors in Rn such that the lp distance between any pair is precisely 1, is at most cpn log n. We prove some upper bounds for other lp norms as well.

AB - We show that for every odd integer p ≥ 1 there is an absolute positive constant cp, so that the maximum cardinality of a set of vectors in Rn such that the lp distance between any pair is precisely 1, is at most cpn log n. We prove some upper bounds for other lp norms as well.

UR - http://www.scopus.com/inward/record.url?scp=0041851195&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0041851195&partnerID=8YFLogxK

U2 - 10.1007/s00039-003-0418-7

DO - 10.1007/s00039-003-0418-7

M3 - Article

AN - SCOPUS:0041851195

VL - 13

SP - 467

EP - 482

JO - Geometric and Functional Analysis

JF - Geometric and Functional Analysis

SN - 1016-443X

IS - 3

ER -