4 citations · 7 across the 7 of their papers we have counts for
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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…
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…
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…