Czechoslovak Mathematical Journal, Vol. 68, No. 3, pp. 853-874, 2018


On realizability of sign patterns by real polynomials

Vladimir Kostov

Received April 7, 2017.   Published online May 15, 2018.

Abstract:  The classical Descartes' rule of signs limits the number of positive roots of a real polynomial in one variable by the number of sign changes in the sequence of its coefficients. One can ask the question which pairs of nonnegative integers $(p,n)$, chosen in accordance with this rule and with some other natural conditions, can be the pairs of numbers of positive and negative roots of a real polynomial with prescribed signs of the coefficients. The paper solves this problem for degree $8$ polynomials.
Keywords:  real polynomial in one variable; sign pattern; Descartes' rule of signs
Classification MSC:  26C10, 30C15


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Affiliations:   Vladimir Kostov, Université Côte d'Azur, Laboratoire de Mathématiques, Parc Valrose, 06108 Nice cedex 2, France, e-mail: vladimir.kostov@unice.fr


 
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