The \(D_4\) Root System is Not Universally Optimal

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The \(D_4\) Root System is Not Universally Optimal

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dc.contributor.author Cohn, Henry
dc.contributor.author Kumar, Abhinav
dc.contributor.author Conway, John H.
dc.contributor.author Elkies, Noam
dc.date.accessioned 2009-04-13T16:34:27Z
dc.date.issued 2007
dc.identifier.citation Cohn, Henry, John H. Conway, Noam D. Elkies, and Abhinav Kumar. 2007. The \(D_4\) root system is not universally optimal. Experimental Mathematics 16(3): 313-320. en
dc.identifier.issn 1058-6458 en
dc.identifier.uri http://nrs.harvard.edu/urn-3:HUL.InstRepos:2794814
dc.description.abstract We prove that the \(D_4\) root system (equivalently, the set of vertices of the regular 24-cell) is not a universally optimal spherical code. We further conjecture that there is no universally optimal spherical code of 24 points in \(S^3\), based on numerical computations suggesting that every 5-design consisting of 24 points in \(S^3\) is in a 3-parameter family (which we describe explicitly, based on a construction due to Sali) of deformations of the \(D_4\) root system. en
dc.description.sponsorship Mathematics en
dc.publisher AK Peters en
dc.relation.isversionof http://akpeters.metapress.com/content/n1700h637u4tk136 en
dash.license LAA
dc.title The \(D_4\) Root System is Not Universally Optimal en
dc.relation.journal Experimental mathematics en
dash.depositing.author Elkies, Noam

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  • FAS Scholarly Articles [7289]
    Peer reviewed scholarly articles from the Faculty of Arts and Sciences of Harvard University

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