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A converse to the Grace-Walsh-Szegö theorem
Stockholm University, Faculty of Science, Department of Mathematics.
Waterloo.
2009 (English)In: Mathematical proceedings of the Cambridge Philosophical Society (Print), ISSN 0305-0041, E-ISSN 1469-8064, Vol. 147, no 2, 447-453 p.Article in journal (Refereed) Published
Abstract [en]

We prove that the symmetrizer of a permutation group preserves stability if and only if the group is orbit homogeneous. A consequence is that the hypothesis of permutation invariance in the Grace–Walsh–Szegő Coincidence Theorem cannot be relaxed. In the process we obtain a new characterization of the Grace-like polynomials, introduced by D. Ruelle, and prove that the class of such polynomials can be endowed with a natural multiplication.

Place, publisher, year, edition, pages
2009. Vol. 147, no 2, 447-453 p.
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Mathematics
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URN: urn:nbn:se:su:diva-35115DOI: 10.1017/S0305004109002424OAI: oai:DiVA.org:su-35115DiVA: diva2:286441
Available from: 2010-01-14 Created: 2010-01-14 Last updated: 2017-12-12Bibliographically approved

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