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

24 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 - 2003
Externally published	Yes

All Science Journal Classification (ASJC) codes

Analysis
Geometry and Topology

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10.1007/s00039-003-0418-7

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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",

note = "Funding Information: The first author{\textquoteright}s research is supported in part by a State of New Jersey grant, by a USA Israeli BSF grant, by a grant from the Israel Science Foundation and by the Hermann Minkowski Minerva Center for Geometry at Tel Aviv University. The second author{\textquoteright}s research is supported in part by grant No. A1019901 of the Academy of Sciences of the Czech Republic and by project No. LN00A056 of the Ministry of Education of the Czech Republic. Part of this research was done while the author was visiting IAS, Princeton.",

year = "2003",

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

language = "English (US)",

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journal = "Geometric and Functional Analysis",

issn = "1016-443X",

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TY - JOUR

T1 - Equilateral sets in lpn

AU - Alon, Noga

AU - Pudlák, Pavel

N1 - Funding Information: The first author’s research is supported in part by a State of New Jersey grant, by a USA Israeli BSF grant, by a grant from the Israel Science Foundation and by the Hermann Minkowski Minerva Center for Geometry at Tel Aviv University. The second author’s research is supported in part by grant No. A1019901 of the Academy of Sciences of the Czech Republic and by project No. LN00A056 of the Ministry of Education of the Czech Republic. Part of this research was done while the author was visiting IAS, Princeton.

PY - 2003

Y1 - 2003

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.

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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 -

Equilateral sets in l_pⁿ

Abstract

All Science Journal Classification (ASJC) codes

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