1 citations · 1 across the 10 of their papers we have counts for
12 papers
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.…
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…
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…
Unsensed enumeration of cubic unicellular maps on orientable and non-orientable surfaces
Alexander Omelchenko, Igor Labutin
We enumerate cubic (3-regular) unicellular maps on closed surfaces up to all homeomorphisms. Using the orbifold approach, we reduce the unsensed enumeration to explicit counts of q…
Enumeration of Unsensed Orientable Maps on Surfaces of a Given Genus
Evgeniy Krasko, Alexander Omelchenko
In this work for the first time we enumerate unlabelled maps on orientable genus surfaces with respect to all homeomorphisms, including both orientation-preserving and orientat…
Enumeration of -regular Maps on the Torus. Part II: Enumeration of Unsensed Maps
Evgeniy Krasko, Alexander Omelchenko
The second part of the paper is devoted to enumeration of -regular toroidal maps up to all homeomorphisms of the torus (unsensed maps). We describe in detail the periodic orient…