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

DSpace/Manakin Repository

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

Show simple item record Cohn, Henry Kumar, Abhinav Conway, John H. Elkies, Noam 2009-04-13T16:34:27Z 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.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 en
dash.license LAA
dc.title The \(D_4\) Root System is Not Universally Optimal en
dc.relation.journal Experimental mathematics en Elkies, Noam

Files in this item

Files Size Format View xmlui.dri2xhtml.METS-1.0.item-files-description
Elkies - The D4 Root System.pdf 167.0Kb PDF View/Open Elkies' paper on The D4 Root System

This item appears in the following Collection(s)

Show simple item record


Search DASH

Advanced Search