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math.GT2024
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…
math.CO2024
Groups of permutations preserving orientation (parity) of subsets of a fixed size, and related monoids
Vitor Fernandes, Alexei Vernitski
We study permutations on n elements preserving orientation (parity) of every subset of size k. We describe all groups of these permutations. Unexpectedly, these groups (except for…