3 papers
math.GT2026
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…
math.CO2025
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…
math.GT2024
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…