4 citations · 8 across the 10 of their papers we have counts for
5 papers · 1 filter
Gauss diagrams as cubic graphs: The choice of the Hamiltonian cycle matters
Alexei Vernitski
We explore to what extent the properties of a Gauss diagram are affected by the choice of its Hamiltonian cycle. We present an example of a realizable Gauss diagram and an unrealiz…
Automated reasoning for proving non-orderability of groups
Alexei Lisitsa, Zipei Nie, Alexei Vernitski
We demonstrate how a generic automated theorem prover can be applied to establish the non-orderability of groups. Our approach incorporates various tools such as positive cones, to…
Machine learning discovers invariants of braids and flat braids
Alexei Lisitsa, Mateo Salles, Alexei Vernitski
We use machine learning to classify examples of braids (or flat braids) as trivial or non-trivial. Our ML takes form of supervised learning using neural networks (multilayer percep…
Circle graphs (chord interlacement graphs) of Gauss diagrams: Descriptions of realizable Gauss diagrams, algorithms, enumeration
Abdullah Khan, Alexei Lisitsa, Viktor Lopatkin +1
Chord diagrams, under the name of Gauss diagrams, are used in low-dimensional topology as an important tool for studying curves or knots. Those Gauss diagrams that correspond to cu…
Experimental Mathematics Approach to Gauss Diagrams Realizability
A. Khan, A. Lisitsa, A. Vernitski
A Gauss diagram (or, more generally, a chord diagram) consists of a circle and some chords inside it. Gauss diagrams are a well-established tool in the study of topology of knots a…