A converse to the Grace-Walsh-Szegö theorem
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
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.
IdentifiersURN: urn:nbn:se:su:diva-35115DOI: 10.1017/S0305004109002424OAI: oai:DiVA.org:su-35115DiVA: diva2:286441