Abstract
Which polynomials are minimal polynomials of integer symmetric matrices? There are some easy necessary conditions, and for degrees up to 4 a theorem of Estes and Guralnick implies that these conditions are in fact sufficient. This theorem led them to conjecture that the same would hold for larger degrees too. In this chapter, estimates involving the discriminant, span and trace are used to find counterexamples to the Estes–Guralnick Conjecture for every degree greater than 5. The case of degree 5 is still open.
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McKee, J., Smyth, C. (2021). Minimal Polynomials of Integer Symmetric Matrices. In: Around the Unit Circle. Universitext. Springer, Cham. https://doi.org/10.1007/978-3-030-80031-4_21
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DOI: https://doi.org/10.1007/978-3-030-80031-4_21
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Publisher Name: Springer, Cham
Print ISBN: 978-3-030-80030-7
Online ISBN: 978-3-030-80031-4
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