6 citations · 8 across the 9 of their papers we have counts for
9 papers
About the number of connected components in arrangements of hyperplanes
I. Shnurnikov
We consider arrangements of n hyperplanes of codimension one in a real projective space of dimension d. Let us denote by F the maximal possible number f of connected components of…
What is the number of decompositions of torus into given number of regions by unions of geodesics?
I. Shnurnikov
We prove some preliminary results concerning two questions of O.Karpenkov: (1) What is the number of decompositions of torus of dimension 2 into given number f of regions by unions…
Realizability of singular levels of Morse functions by unions of geodesics
I. Shnurnikov
We list special graphs of degree 4 with at most 3 vertices (atoms from the theory of integrable hamiltonian systems) which could be represented by a union of closed geodesics on th…
On the number of connected components of complements to arrangements of subtori
I. Shnurnikov
We consider the arrangements of subtori in a flat d - dimensional torus T. Let us consider an arrangement on n subtori of codimension one, let f be the number of connected componen…
On the number of hyperbolic manifolds of complexity n
A. Magazinov, I. Shnurnikov
We consider hyperbolic manifolds with boundary, which admit an ideal triangulation with n ideal triangles and one edge. We prove that the number of these manifolds is $\exp(n\ln(n)…
On the number of connected components in complements to arrangements of submanifolds
I. N. Shnurnikov
We consider arrangements of n connected codimensional one submanifolds in closed d-dimensional manifold M. Let f be the number of connected components of the complement in M to the…
Existence of a line without real points in quadric intersection
I. Shnurnikov
The topology of the intersection of three quadrics in Euclidean 6-space is studied using Kollar results. This needs an existence of a line without real points in the complex projec…
On the number of regions and multiplicities of vertices in plane arrangements
Igor Shnurnikov
For an arrangement of pseudolines in the real projective plane let us denote by the number of vertices incident to lines. We obtain a linear on inequality simil…
On a sum of centered random variables with nonreducing variances
I. Shnurnikov
We give a new proof of weak version of R. Holzman and D.J. Kleitman bound on a number of the -dimensional cube vertices strictly separated by a hyperplane, tangent to the inscri…