Paper Image

Groups preserving subset orientation

Published on:

8 February 2024

Primary Category:

Combinatorics

Paper Authors:

Alexei Vernitski

Bullets

Key Details

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

AI generated summary

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.

Answers from this paper

Comments

No comments yet, be the first to start the conversation...

Sign up to comment on this paper

Sign Up