8 February 2024
Studies permutations preserving parity of k-subsets
Generalizes order/orientation-preserving semigroups
Finds these permutation groups are trivial, cyclic or dihedral
Provides formulas for group sizes based on k and n
Groups preserving subset orientation
This paper studies permutations on a set that preserve the parity (even/odd count) of inversions of every subset of a fixed size k. It finds that, perhaps surprisingly, most of these permutation groups are trivial, cyclic, or dihedral. The paper generalizes semigroups of order-preserving and orientation-preserving mappings.
No comments yet, be the first to start the conversation...
Sign up to comment on this paper