Lower bound for the Perron-Frobenius degrees of Perron numbers
Abstract
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. 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 biPerron numbers.
- Publication:
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arXiv e-prints
- Pub Date:
- November 2017
- DOI:
- 10.48550/arXiv.1711.06885
- arXiv:
- arXiv:1711.06885
- Bibcode:
- 2017arXiv171106885Y
- Keywords:
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- Mathematics - Geometric Topology
- E-Print:
- To appear in Ergodic Theory and Dynamical Systems, 15 pages, 4 figures