The \(D_4\) Root System is Not Universally Optimal
| Title: | The \(D_4\) Root System is Not Universally Optimal |
| Author: |
Cohn, Henry; Kumar, Abhinav; Conway, John H.; Elkies, Noam
Note: Order does not necessarily reflect citation order of authors. |
| 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. |
| Full Text & Related Files: |
Elkies - The D4 Root System.pdf (171.0Kb; PDF) 
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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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