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

Dmitriy Bilyk, Ryan W. Matzke

Research output: Contribution to journalArticlepeer-review

5 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 languageEnglish (US)
Pages (from-to)51-59
Number of pages9
JournalProceedings of the American Mathematical Society
Volume147
Issue number1
DOIs
StatePublished - Jan 2019

Bibliographical note

Funding Information:
Received by the editors January 23, 2018. 2010 Mathematics Subject Classification. Primary 11K38, 52C35. This work is supported by the NSF grant DMS 1665007 (the first author) and the NSF Graduate Research Fellowship 00039202 (the second author).

Publisher Copyright:
© 2018, American Mathematical Society.

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