A converse to the Grace–Walsh–Szegő theorem
| Autor: | David G. Wagner, Petter Brändén |
|---|---|
| Rok vydání: | 2009 |
| Předmět: |
Class (set theory)
Polynomial Group (mathematics) General Mathematics 010102 general mathematics 010103 numerical & computational mathematics Permutation group Characterization (mathematics) 01 natural sciences Combinatorics Converse Multiplication 0101 mathematics Orbit (control theory) Mathematics |
| Zdroj: | Mathematical Proceedings of the Cambridge Philosophical Society. 147:447-453 |
| ISSN: | 1469-8064 0305-0041 |
| DOI: | 10.1017/s0305004109002424 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|