3 papers
math.CO2026
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…
math.NT2025
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…
math.CO2025
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…