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dc.contributor.authorBlekherman, Grigoriy
dc.contributor.authorRiener, Cordian
dc.date.accessioned2020-05-22T07:04:18Z
dc.date.available2020-05-22T07:04:18Z
dc.date.issued2020-05-21
dc.description.abstractWe study symmetric non-negative forms and their relationship with symmetric sums of squares. For a fixed number of variables <i>n</i> and degree 2<i>d</i>, symmetric non-negative forms and symmetric sums of squares form closed, convex cones in the vector space of <i>n</i>-variate symmetric forms of degree 2<i>d</i>. Using representation theory of the symmetric group we characterize both cones in a uniform way. Further, we investigate the asymptotic behavior when the degree 2<i>d</i> is fixed and the number of variables <i>n</i> grows. Here, we show that, in sharp contrast to the general case, the difference between symmetric non-negative forms and sums of squares does not grow arbitrarily large for any fixed degree 2<i>d</i>. We consider the case of symmetric quartic forms in more detail and give a complete characterization of quartic symmetric sums of squares. Furthermore, we show that in degree 4 the cones of non-negative symmetric forms and symmetric sums of squares approach the same limit, thus these two cones asymptotically become closer as the number of variables grows. We conjecture that this is true in arbitrary degree 2<i>d</i>.en_US
dc.identifier.citationBlekherman G, Riener C. Symmetric Non-Negative Forms and Sums of Squares. Discrete & Computational Geometry. 2020en_US
dc.identifier.cristinIDFRIDAID 1812079
dc.identifier.doihttps://doi.org/10.1007/s00454-020-00208-w
dc.identifier.issn0179-5376
dc.identifier.issn1432-0444
dc.identifier.urihttps://hdl.handle.net/10037/18356
dc.language.isoengen_US
dc.publisherSpringeren_US
dc.relation.journalDiscrete & Computational Geometry
dc.relation.urihttps://link.springer.com/article/10.1007%2Fs00454-020-00208-w#article-info
dc.rights.accessRightsopenAccessen_US
dc.rights.holderCopyright 2020 The Author(s)en_US
dc.subjectVDP::Mathematics and natural science: 400en_US
dc.subjectVDP::Matematikk og Naturvitenskap: 400en_US
dc.subjectVDP::Technology: 500en_US
dc.subjectVDP::Teknologi: 500en_US
dc.titleSymmetric Non-Negative Forms and Sums of Squaresen_US
dc.type.versionpublishedVersionen_US
dc.typeJournal articleen_US
dc.typeTidsskriftartikkelen_US
dc.typePeer revieweden_US


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