Geodesic
On realizability of sign patterns by real polynomials
Czechoslovak Mathematical Journal, Tome 68 (2018) no. 3, pp. 853-874.

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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.
DOI : 10.21136/CMJ.2018.0163-17
Classification : 26C10, 30C15
Keywords: real polynomial in one variable; sign pattern; Descartes' rule of signs 
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     title = {On realizability of sign patterns by real polynomials},
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Kostov, Vladimir. On realizability of sign patterns by real polynomials. Czechoslovak Mathematical Journal, Tome 68 (2018) no. 3, pp. 853-874. doi : 10.21136/CMJ.2018.0163-17. http://geodesic.mathdoc.fr/articles/10.21136/CMJ.2018.0163-17/

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