A converse to the Grace-Walsh-Szego theorem
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
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.
IdentifiersURN: urn:nbn:se:kth:diva-18711DOI: 10.1017/s0305004109002424ISI: 000269277400013ScopusID: 2-s2.0-70450245515OAI: oai:DiVA.org:kth-18711DiVA: diva2:336758
QC 201005252010-08-052010-08-052010-12-15Bibliographically approved