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A converse to the Grace--Walsh--Szeg\H{o} theorem
- Publication Year :
- 2008
-
Abstract
- We prove that the symmetrizer of a permutation group preserves stability of a polynomial if and only if the group is orbit homogeneous. A consequence is that the hypothesis of permutation invariance in the Grace-Walsh-Szeg\H{o} Coincidence Theorem cannot be relaxed. In the process we obtain a new characterization of the \emph{Grace-like polynomials} introduced by D. Ruelle, and prove that the class of such polynomials can be endowed with a natural multiplication.<br />Comment: 7 pages
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.0809.3225
- Document Type :
- Working Paper
- Full Text :
- https://doi.org/10.1017/S0305004109002424