Publikation: A note on extrema of linear combinations of elementary symmetric functions
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2012
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Linear and Multilinear Algebra. 2012, 60(2), pp. 219-224. ISSN 0308-1087. Available under: doi: 10.1080/03081087.2011.588438
Zusammenfassung
This note provides a new approach to a result of Foregger [T.H. Foregger, On the relative extrema of a linear combination of elementary symmetric functions, Linear Multilinear Algebra 20 (1987) pp. 377–385] and related earlier results by Keilson [J. Keilson, A theorem on optimum allocation for a class of symmetric multilinear return functions, J. Math. Anal. Appl. 15 (1966), pp. 269–272] and Eberlein [P.J. Eberlein, Remarks on the van der Waerden conjecture, II, Linear Algebra Appl. 2 (1969), pp. 311–320]. Using quite different techniques, we prove a more general result from which the others follow easily. Finally, we argue that the proof in [Foregger, 1987] is flawed.
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Fachgebiet (DDC)
510 Mathematik
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Extrema, elementary symmetric functions, hyperbolic polynomials, elementary symmetric functions
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KOVAČEC, Alexander, Salma KUHLMANN, Cordian RIENER, 2012. A note on extrema of linear combinations of elementary symmetric functions. In: Linear and Multilinear Algebra. 2012, 60(2), pp. 219-224. ISSN 0308-1087. Available under: doi: 10.1080/03081087.2011.588438BibTex
@article{Kovacec2012extre-17626,
year={2012},
doi={10.1080/03081087.2011.588438},
title={A note on extrema of linear combinations of elementary symmetric functions},
number={2},
volume={60},
issn={0308-1087},
journal={Linear and Multilinear Algebra},
pages={219--224},
author={Kovačec, Alexander and Kuhlmann, Salma and Riener, Cordian}
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