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Which Sign Patterns are Canonical?

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Abstract

We consider real polynomials in one variable without vanishing coefficients, with all roots real and of distinct moduli. We show that the signs of the coefficients define the order of the moduli of the roots on the real positive half-line exactly when no four consecutive signs of coefficients equal \((+,+,-,-)\), \((-,-,+,+)\), \((+,-,-,+)\) or \((-,+,+,-)\).

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  1. LJAD, CNRS, Université Côte d’Azur, Nice, France

    Vladimir Petrov Kostov

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  1. Vladimir Petrov Kostov
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Correspondence to Vladimir Petrov Kostov.

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Kostov, V.P. Which Sign Patterns are Canonical?. Results Math 77, 235 (2022). https://doi.org/10.1007/s00025-022-01769-3

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