Search engine for discovering works of Art, research articles, and books related to Art and Culture
Javascript must be enabled to continue!
Lower bound for the Perron–Frobenius degrees of Perron numbers
View through CrossRef
Using an idea of Doug Lind, we give a lower bound for the Perron–Frobenius degree of a Perron number that is not totally real, in terms of the layout of its Galois conjugates in the complex plane. As an application, we prove that there are cubic Perron numbers whose Perron–Frobenius degrees are arbitrary large, a result known to Lind, McMullen and Thurston. A similar result is proved for bi-Perron numbers.
Title: Lower bound for the Perron–Frobenius degrees of Perron numbers
Description:
Using an idea of Doug Lind, we give a lower bound for the Perron–Frobenius degree of a Perron number that is not totally real, in terms of the layout of its Galois conjugates in the complex plane.
As an application, we prove that there are cubic Perron numbers whose Perron–Frobenius degrees are arbitrary large, a result known to Lind, McMullen and Thurston.
A similar result is proved for bi-Perron numbers.
Related Results
Variations catégorielles sur les quantales de Frobenius
Variations catégorielles sur les quantales de Frobenius
Categorical variations on Frobenius quantales
L'objectif premier de cette thèse est d'étudier d'un point de vue catégorique le théorème suivant : un treillis est co...
Extensions of Perron-Frobenius Theory
Extensions of Perron-Frobenius Theory
Από το 1907, ο Oskar Perron απέδειξε ένα θεώρημα για θετικούς πίνακες, το οποίο επεκτάθηκε από τον Georg Frobenius το 1912 για μη αναγώγιμους μη αρνητικούς πίνακες. Στη συνέχεια αν...
On Frobenius and separable algebra extensions in monoidal categories: applications to wreaths
On Frobenius and separable algebra extensions in monoidal categories: applications to wreaths
We characterize Frobenius and separable monoidal algebra extensions
i: R \to S
in terms given by...
On Two-Dimensional Closed–Open Topological Field Theories
On Two-Dimensional Closed–Open Topological Field Theories
Topological field theories (TFTs) have captured the attention of mathematicians due to their various applications. In categorical terms, an nTFT is defined as a monoidal functor th...
Twin TQFTs and Frobenius Algebras
Twin TQFTs and Frobenius Algebras
We introduce the category of singular 2-dimensional cobordisms and show that it admits a completely algebraic description as the free symmetric monoidal category on atwin Frobenius...
A Class of Local Non-Chain Rings of Order p5m
A Class of Local Non-Chain Rings of Order p5m
This study investigates finite commutative local non-chain rings characterized by the well-established invariants p, n, m, l, and k, where p denotes a prime number. We specifically...
Frobenius Local Rings of Length 5 and Index of Nilpotency 3
Frobenius Local Rings of Length 5 and Index of Nilpotency 3
This paper investigates finite local non-chain rings associated by the well-known invariants p,n,m,l, and k, where p is a prime number. In particular, we provide a comprehensive ch...
Varieties with ample Frobenius-trace kernel
Varieties with ample Frobenius-trace kernel
In the search of a projective analog of Kunz’s theorem and a Frobenius-theoretic analog of Mori–Hartshorne’s theorem, we investigate the positivity of the kernel of the Frobenius t...