Equiangular Lines in Euclidean Spaces: Dimensions 17 and 18

Gary R.W. Greaves; Jeven Syatriadi; Pavlo Yatsyna

doi:10.1090/mcom/3832

Equiangular Lines in Euclidean Spaces: Dimensions 17 and 18

Gary R.W. Greaves^*, Jeven Syatriadi, Pavlo Yatsyna

^*Tämän työn vastaava kirjoittaja

Tutkimustuotos: Lehtiartikkeli › Article › Scientific › vertaisarvioitu

4 Sitaatiot (Scopus)

Abstrakti

We show that the maximum cardinality of an equiangular line system in 17 dimensions is 48, thereby solving a longstanding open problem.

Alkuperäiskieli	Englanti
Sivut	1867-1903
Sivumäärä	37
Julkaisu	Mathematics of Computation
Vuosikerta	92
Numero	342
DOI - pysyväislinkit	https://doi.org/10.1090/mcom/3832
Tila	Julkaistu - 8 maalisk. 2023
OKM-julkaisutyyppi	A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä

Rahoitus

Received by the editor July 29, 2021, and, in revised form, May 17, 2022, September 11, 2022, January 4, 2023, and January 16, 2023. 2020 Mathematics Subject Classification. Primary 05B40; Secondary 05B20. Key words and phrases. Equiangular lines, dimensions 17 and 18, compatible polynomials, eigenspace angles, polynomial interlacing. The first author was supported in part by the Singapore Ministry of Education Academic Research Fund (Tier 1); grant numbers: RG29/18 and RG21/20. The third author was supported in part by the project PRIMUS/20/SCI/002 from Charles University.

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10.1090/mcom/3832

https://arxiv.org/abs/2104.04330

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title = "Equiangular Lines in Euclidean Spaces: Dimensions 17 and 18",

abstract = "We show that the maximum cardinality of an equiangular line system in 17 dimensions is 48, thereby solving a longstanding open problem.",

keywords = "compatible polynomials, dimensions 17 and 18, eigenspace angles, Equiangular lines, polynomial interlacing",

author = "Greaves, \{Gary R.W.\} and Jeven Syatriadi and Pavlo Yatsyna",

note = "Funding Information: Received by the editor July 29, 2021, and, in revised form, May 17, 2022, September 11, 2022, January 4, 2023, and January 16, 2023. 2020 Mathematics Subject Classification. Primary 05B40; Secondary 05B20. Key words and phrases. Equiangular lines, dimensions 17 and 18, compatible polynomials, eigenspace angles, polynomial interlacing. The first author was supported in part by the Singapore Ministry of Education Academic Research Fund (Tier 1); grant numbers: RG29/18 and RG21/20. The third author was supported in part by the project PRIMUS/20/SCI/002 from Charles University. Publisher Copyright: {\textcopyright} 2023 American Mathematical Society",

year = "2023",

month = mar,

day = "8",

doi = "10.1090/mcom/3832",

language = "English",

volume = "92",

pages = "1867--1903",

journal = "Mathematics of Computation",

issn = "0025-5718",

publisher = "American Mathematical Society",

number = "342",

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T1 - Equiangular Lines in Euclidean Spaces: Dimensions 17 and 18

AU - Greaves, Gary R.W.

AU - Syatriadi, Jeven

AU - Yatsyna, Pavlo

N1 - Funding Information: Received by the editor July 29, 2021, and, in revised form, May 17, 2022, September 11, 2022, January 4, 2023, and January 16, 2023. 2020 Mathematics Subject Classification. Primary 05B40; Secondary 05B20. Key words and phrases. Equiangular lines, dimensions 17 and 18, compatible polynomials, eigenspace angles, polynomial interlacing. The first author was supported in part by the Singapore Ministry of Education Academic Research Fund (Tier 1); grant numbers: RG29/18 and RG21/20. The third author was supported in part by the project PRIMUS/20/SCI/002 from Charles University. Publisher Copyright: © 2023 American Mathematical Society

PY - 2023/3/8

Y1 - 2023/3/8

N2 - We show that the maximum cardinality of an equiangular line system in 17 dimensions is 48, thereby solving a longstanding open problem.

AB - We show that the maximum cardinality of an equiangular line system in 17 dimensions is 48, thereby solving a longstanding open problem.

KW - compatible polynomials

KW - dimensions 17 and 18

KW - eigenspace angles

KW - Equiangular lines

KW - polynomial interlacing

UR - https://www.scopus.com/pages/publications/85152642965

UR - https://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=aalto_pure&SrcAuth=WosAPI&KeyUT=WOS:000947078700001&DestLinkType=FullRecord&DestApp=WOS

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DO - 10.1090/mcom/3832

M3 - Article

AN - SCOPUS:85152642965

SN - 0025-5718

VL - 92

SP - 1867

EP - 1903

JO - Mathematics of Computation

JF - Mathematics of Computation

IS - 342

ER -

Equiangular Lines in Euclidean Spaces: Dimensions 17 and 18

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