4 papers
Minimum number of partial triangulations
Andrey Kupavskii, Aleksei Volostnov, Yury Yarovikov
We show that the number of partial triangulations of a set of points on the plane is at least the -nd Catalan number. This is tight for convex -gons. We also describe…
Wiener index and graphs, almost half of whose vertices satisfy Šoltés property
Margarita Akhmejanova, Konstantin Olmezov, Aleksei Volostnov +3
The Wiener index of a connected graph is a sum of distances between all pairs of vertices of . In 1991, Šoltés formulated the problem of finding all graphs such t…
On some double sums with multiplicative characters
Aleksei S. Volostnov
We obtain a new upper bound for binary sums with multiplicative characters over variables belong to some sets, having small additive doubling.
Sums of multiplicative characters with additive convolutions
Ilya D. Shkredov, Aleksei S. Volostnov
In the paper we obtain new estimates for binary and ternary sums of multiplicative characters with additive convolutions of characteristic functions of sets, having small additive…