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cs.DM2026
Exhaustive Generation of Genus-One Knot and Link Diagrams via Maps on the Torus
Alexander Omelchenko
We present an algorithmic framework for the exhaustive generation and tabulation of knot and link diagrams on the thickened torus T^2 x I, based on the theory of maps on surfaces.…
math.DS2026
Threshold Dynamics of Voter Radicalization on the Probability Simplex
Alexander Omelchenko
We analyse two coupled ODE models of political competition on invariant probability simplices with a conserved electorate. The baseline three-group model tracks left-radical, centr…
math.CO2026
Maps on Surfaces and the Tabulation of Knots and Links in the Thickened Torus Through Ten Crossings
Alexander Omelchenko
We give a combinatorial tabulation of knots and links in the thickened torus based on the theory of maps on surfaces: cellular -regular torus projections are enco…