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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Title: The \(D_4\) Root System is Not Universally Optimal
Author: Cohn, Henry; Kumar, Abhinav; Conway, John H.; Elkies, Noam

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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.
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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.
Published Version: http://akpeters.metapress.com/content/n1700h637u4tk136
Terms of Use: This article is made available under the terms and conditions applicable to Other Posted Material, as set forth at http://nrs.harvard.edu/urn-3:HUL.InstRepos:dash.current.terms-of-use#LAA
Citable link to this page: http://nrs.harvard.edu/urn-3:HUL.InstRepos:2794814

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  • FAS Scholarly Articles [7374]
    Peer reviewed scholarly articles from the Faculty of Arts and Sciences of Harvard University
 
 

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