On Descartes’ rule for polynomials with two variations of signs

For sequences of d + 1 signs + and − beginning with a + and having exactly two variations of sign, we give some sufficient conditions for the (non)existence of degree d real univariate polynomials with such signs of the coefficients and having given numbers of positive and negative roots compatible...

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Veröffentlicht in:	Lithuanian mathematical journal 2020-10, Vol.60 (4), p.456-469
Hauptverfasser:	Cheriha, Hassen, Gati, Yousra, Kostov, Vladimir Petrov
Format:	Artikel
Sprache:	eng
Schlagworte:	Actuarial Sciences Mathematics Mathematics and Statistics Number Theory Ordinary Differential Equations Polynomials Probability Theory and Stochastic Processes
Online-Zugang:	Volltext
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Beschreibung
Zusammenfassung:	For sequences of d + 1 signs + and − beginning with a + and having exactly two variations of sign, we give some sufficient conditions for the (non)existence of degree d real univariate polynomials with such signs of the coefficients and having given numbers of positive and negative roots compatible with Descartes’ rule of signs.
ISSN:	0363-1672 1573-8825
DOI:	10.1007/s10986-020-09491-9