6 citations · 8 across the 9 of their papers we have counts for
4 papers · 1 filter
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…
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 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…