Groups of permutations that are even on subsets of a fixed size, and related monoids
Vítor Hugo Fernandes, Alexei Vernitski · International Journal of Algebra and Computation · 2025
In this paper, we study permutations on n elements that are even on every subset of size t. We describe all groups of these permutations. Unexpectedly, these groups (except for some special cases) are either trivial, cyclic or dihedral. In this context, we define and study monoids that generalize both monoids of order-preserving mappings and monoids of orientation-preserving mappings.