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A converse to the Grace-Walsh-Szego theorem
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).ORCID iD: 0000-0003-1055-1474
2009 (English)In: Mathematical proceedings of the Cambridge Philosophical Society (Print), ISSN 0305-0041, E-ISSN 1469-8064, Vol. 147, 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-Szego 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, 447-453 p.
Keyword [en]
polynomials
Identifiers
URN: urn:nbn:se:kth:diva-18711DOI: 10.1017/s0305004109002424ISI: 000269277400013Scopus ID: 2-s2.0-70450245515OAI: oai:DiVA.org:kth-18711DiVA: diva2:336758
Note
QC 20100525Available from: 2010-08-05 Created: 2010-08-05 Last updated: 2017-12-12Bibliographically approved

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Bränden, Petter

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