Geodesic
On Root Arrangements of Polynomial-Like Functions and their Derivatives
Serdica Mathematical Journal, Tome 31 (2005) no. 3, pp. 201-216 Cet article a éte moissonné depuis la source Bulgarian Digital Mathematics Library

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We show that for n = 4 they are realizable either by hyperbolic polynomials of degree 4 or by non-hyperbolic polynomials of degree 6 whose fourth derivatives never vanish (these are a particular case of the so-called hyperbolic polynomial-like functions of degree 4).
Keywords: Hyperbolic Polynomial, Root Arrangement, Configuration Vector 
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     author = {Kostov, Vladimir},
     title = {On {Root} {Arrangements} of {Polynomial-Like} {Functions} and their {Derivatives}},
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Kostov, Vladimir. On Root Arrangements of Polynomial-Like Functions and their Derivatives. Serdica Mathematical Journal, Tome 31 (2005) no. 3, pp. 201-216. http://geodesic.mathdoc.fr/item/SMJ2_2005_31_3_a2/