4 citations · 7 across the 7 of their papers we have counts for
9 papers
Explicit formula for the Rasmussen invariant of odd pretzel knots
Yury Belousov, Vadim Stepaniuk
We compute the Rasmussen s-invariant for all odd pretzel knots, giving an explicit closed formula. The formula extends to all slice-torus invariants that are invariant under mutati…
S-meandric Permutations and Tangency Polynomials
Yury Belousov, Viktoriia Georgievskaia
A meander is a configuration of two simple plane curves intersecting transversely. The orders of their intersection points define a permutation that determines the configuration. W…
Explicit Formulas for the Alexander Polynomial of Pretzel Knots
Y. Belousov
We provide explicit formulas for the Alexander polynomial of pretzel knots and establish several immediate corollaries, including the characterization of pretzel knots with a trivi…
Meander diagrams of virtual knots
Y. Belousov, V. Chernov, A. Malyutin +1
For classical knots, there is a concept of (semi)meander diagrams; in this short note we generalize this concept to virtual knots and prove that the classes of meander and semimean…
The 2-colored operad on the set of singular meanders
Yury Belousov
In the recent work arXiv:2112.10289 we introduced a geometric decomposition of meanders. In the present paper, we generalize this approach to the case of singular meanders and give…
Prime Factorization of Meanders
Y. Belousov
In this paper, we introduce a prime factorization of open meanders, articulated through the framework of 2-colored operads. We demonstrate that each open meander can be canonically…
On irreducible meanders growth rate
Y. Belousov, A. Malyutin
In this article, we provide upper and lower bounds for the growth rate of irreducible meanders. The obtained upper bound implies that the proportion of irreducible meanders among a…
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…
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…