2 citations · 6 across the 5 of their papers we have counts for
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On arrangements of the roots of a hyperbolic polynomial and of one of its derivatives
Vladimir Petrov Kostov
We consider real monic {\em hyperbolic} polynomials in one real variable, i.e. polynomials having only real roots. Call {\em hyperbolicity domain} of the family of polynomials…
On a stratification defined by real roots of polynomials
Vladimir Petrov Kostov
We consider the family of polynomials , , and the stratification of defined by…
The Deligne-Simpson problem -- a survey
Vladimir Petrov Kostov
The Deligne-Simpson problem (DSP) (resp. the weak DSP) is formulated like this: {\em give necessary and sufficient conditions for the choice of the conjugacy classes $C_j\subset GL…
The connectedness of some varieties and the Deligne-Simpson problem
Vladimir Petrov Kostov
The Deligne-Simpson problem (DSP) (resp. the weak DSP) is formulated like this: {\em give necessary and sufficient conditions for the choice of the conjugacy classes $C_j\subset GL…
On the weak Deligne-Simpson problem for index of rigidity 2
Vladimir Petrov Kostov
We consider the weak version of the Deligne-Simpson problem: give necessary and sufficient conditions upon the conjugacy classes (resp. $C_j\subset GL(n,…
On arrangements of real roots of a real polynomial and its derivatives
Vladimir Petrov Kostov
We prove that all arrangements (consistent with the Rolle theorem and some other natural restrictions) of the real roots of a real polynomial and of its -th derivative are reali…