On the Fejes TÓth problem about the sum of angles between lines

Dmitriy Bilyk; Ryan W. Matzke

doi:10.1090/proc/14263

On the Fejes TÓth problem about the sum of angles between lines

Dmitriy Bilyk, Ryan W. Matzke

School of Mathematics

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

12 Scopus citations

Abstract

In 1959 Fejes Tóth posed a conjecture that the sum of pairwise nonobtuse angles between N unit vectors in S ^d is maximized by periodically repeated elements of the standard orthonormal basis. We obtain new improved upper bounds for this sum, as well as for the corresponding energy integral. We also provide several new approaches to the only settled case of the conjecture: d = 1.

Original language	English (US)
Pages (from-to)	51-59
Number of pages	9
Journal	Proceedings of the American Mathematical Society
Volume	147
Issue number	1
DOIs	https://doi.org/10.1090/proc/14263
State	Published - Jan 2019

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© 2018, American Mathematical Society.

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10.1090/proc/14263

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abstract = " In 1959 Fejes T{\'o}th posed a conjecture that the sum of pairwise nonobtuse angles between N unit vectors in S d is maximized by periodically repeated elements of the standard orthonormal basis. We obtain new improved upper bounds for this sum, as well as for the corresponding energy integral. We also provide several new approaches to the only settled case of the conjecture: d = 1.",

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On the Fejes TÓth problem about the sum of angles between lines

Abstract

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