On the degree and half-degree principle for symmetric polynomials


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RIENER, Cordian, 2012. On the degree and half-degree principle for symmetric polynomials. In: Journal of Pure and Applied Algebra. 216(4), pp. 850-856. ISSN 0022-4049

@article{Riener2012degre-17510, title={On the degree and half-degree principle for symmetric polynomials}, year={2012}, doi={10.1016/j.jpaa.2011.08.012}, number={4}, volume={216}, issn={0022-4049}, journal={Journal of Pure and Applied Algebra}, pages={850--856}, author={Riener, Cordian} }

<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xmlns:bibo="http://purl.org/ontology/bibo/" xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:dcterms="http://purl.org/dc/terms/" xmlns:xsd="http://www.w3.org/2001/XMLSchema#" > <rdf:Description rdf:about="https://kops.uni-konstanz.de/rdf/resource/123456789/17510"> <dcterms:rights rdf:resource="http://nbn-resolving.org/urn:nbn:de:bsz:352-20140905103605204-4002607-1"/> <dcterms:issued>2012</dcterms:issued> <dcterms:abstract xml:lang="deu">In this note we aim to give a new, elementary proof of a statement that was first proved by Timofte (2003) [15]. It says that a symmetric real polynomial F of degree d in n variables is positive on R^n if and only if it is non-negative on the subset of points with at most max{⌊d/2⌋,2} distinct components. We deduce Timofte’s original statement as a corollary of a slightly more general statement on symmetric optimization problems. The idea that we are using to prove this statement is that of relating it to a linear optimization problem in the orbit space. The fact that for the case of the symmetric group S_n this can be viewed as a question on normalized univariate real polynomials with only real roots allows us to conclude the theorems in a very elementary way. We hope that the methods presented here will make it possible to derive similar statements also in the case of other groups.</dcterms:abstract> <dcterms:title>On the degree and half-degree principle for symmetric polynomials</dcterms:title> <dc:date rdf:datatype="http://www.w3.org/2001/XMLSchema#dateTime">2012-01-18T15:41:23Z</dc:date> <dc:creator>Riener, Cordian</dc:creator> <dc:language>deu</dc:language> <dc:rights>deposit-license</dc:rights> <dcterms:available rdf:datatype="http://www.w3.org/2001/XMLSchema#dateTime">2012-01-18T15:41:23Z</dcterms:available> <dc:contributor>Riener, Cordian</dc:contributor> <dcterms:bibliographicCitation>Ersch. in: Journal of Pure and Applied Algebra ; 216 (2012), 4. - S. 850-856</dcterms:bibliographicCitation> <bibo:uri rdf:resource="http://kops.uni-konstanz.de/handle/123456789/17510"/> </rdf:Description> </rdf:RDF>

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