Non-negative integral matrices with given spectral radius and controlled dimension

DOI10.1017/etds.2021.93OpenAlexW3199123854WikidataQ114118663 ScholiaQ114118663MaRDI QIDQ5868369

Mehdi Yazdi

Publication date: 20 September 2022

Published in: Ergodic Theory and Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2101.09268

zbMATH Keywords

entropyPerron-Frobenius theoryPerron numbersshifts of finite type

Mathematics Subject Classification ID

Eigenvalues, singular values, and eigenvectors (15A18) Positive matrices and their generalizations; cones of matrices (15B48) Symbolic dynamics (37B10) PV-numbers and generalizations; other special algebraic numbers; Mahler measure (11R06) Matrices of integers (15B36) Relations between ergodic theory and number theory (37A44)

Cites Work

• Unnamed Item
• On conjectures of Minkowski and Woods for \(n = 9\)
• Upper bounds for Euclidean minima of algebraic number fields
• The spectra of nonnegative matrices via symbolic dynamics
• New bounds in some transference theorems in the geometry of numbers
• Small polynomial matrix presentations of nonnegative matrices
• Counterexamples to a conjecture of Woods
• A remarkable class of algebraic integers. Proof of a conjecture of Vijayaraghavan
• Algebraic integers whose conjugates lie in the unit circle
• The entropies of topological Markov shifts and a related class of algebraic integers
• The spectra of nonnegative integer matrices via formal power series
• Minkowski’s conjecture, well-rounded lattices and topological dimension
• An Introduction to Symbolic Dynamics and Coding
• Lower bound for the Perron–Frobenius degrees of Perron numbers
• Algebraic Number Theory

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