4 citations · 16 across the 10 of their papers we have counts for
10 papers
Hopf-type Theorems For -neighbors
A. V. Malyutin, I. M. Shirokov
We work within the framework of a program aimed at exploring various extended versions for theorems from a class containing Borsuk-Ulam type theorems, some fixed point theorems, th…
Logarithmic algorithms for fair division problems
Alexandr Grebennikov, Xenia Isaeva, Andrei V. Malyutin +2
We study the algorithmic complexity of fair division problems with a focus on minimizing the number of queries needed to find an approximate solution with desired accuracy. We show…
-manifolds represented by -regular graphs with three Eulerian cycles
Evgeny Fominykh, Andrei Malyutin, Ekaterina Shumakova
We construct and study a new class of compact hyperbolic -manifolds with totally geodesic boundary. The members of are d…
Hyperbolic knots are not generic
Yury Belousov, Andrei Malyutin
We show that the proportion of hyperbolic knots among all of the prime knots of or fewer crossings does not converge to as approaches infinity. Moreover, we show that i…
Hyperbolic links are not generic
Andrei V. Malyutin
We show that if is a nontrivial knot then the proportion of satellites of among all of the prime non-split links of or fewer crossings does not converge to as a…
Neighboring mapping points theorem
Andrei V. Malyutin, Oleg R. Musin
We introduce and study a new family of extensions for the Borsuk-Ulam and topological Radon type theorems. The defining idea for this new family is to replace requirements of the f…
Meander diagrams of knots and spatial graphs: proofs of generalized Jablan--Radović conjectures
Yury Belousov, Andrei Malyutin
We study decomposition into simple arcs (i. e., arcs without self-intersections) for diagrams of knots and spatial graphs. In this paper, it is proved in particular that if no edge…
On the question of genericity of hyperbolic knots
Andrei Malyutin
A well-known conjecture in knot theory says that the percentage of hyperbolic knots amongst all of the prime knots of or fewer crossings approaches as approaches infi…
Poisson--Furstenberg boundaries of fundamental groups of closed 3-manifolds
A. Malyutin, P. Svetlov
We obtain a description of Poisson--Furstenberg boundaries for (random walks on) fundamental groups of compact graph-manifolds. Together with previously known results due to V.A. K…
Boundaries of -free groups
Andrei Malyutin, Tatiana Nagnibeda, Denis Serbin
In this paper we study random walks on a finitely generated group which has a free action on a -tree. We show that if is non-abelian and acts minimally, freel…