6 citations · 14 across the 17 of their papers we have counts for
19 papers
Some petal diagrams of the unknot are hard
Alexei Vernitski
A petal diagram of a knot is a projection with a single multi-crossing and no nested loops; it is encoded by a permutation of the heights of the strands through the multi-crossing.…
Capturing properties of planar diagrams in Lean proof assistant software
Alastair Litterick, Alexei Vernitski, Billy Woods
Automated proof assistants are a technology pre-empting mistakes in mathematics. In our practice we have seen that reasoning about planar diagrams is difficult to both humans and c…
Divisibility rules for integers presented as permutations
Thomas Oliver, Alexei Vernitski
In this note, we represent integers in a type of factoradic notation. Rather than use the corresponding Lehmer code, we will view integers as permutations. Given a pair of integers…
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…
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…
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…