Groups of permutations preserving orientation (parity) of subsets of a fixed size, and related monoids

2024/02/08 by Fernandes, Vitor, Vernitski, Alexei
Engineering · #20B05 #20M20 #Combinatorics (math.CO) #FOS: Mathematics #Group Theory (math.GR) #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.2402.05777

openalex publication_date 2024/02/08 · openalex created_date 2024/02/10 · openalex updated_date 2026/07/28

Abstract

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 some special cases) are either trivial, cyclic or dihedral. In this context, we define and study monoids generalizing monoids of order-preserving mappings and monoids of orientation-preserving mappings.

Related

• On orientation-preserving transformations of a chain
• On orientation-preserving transformations of a chain
• The monoid of all injective orientation preserving partial transformations on a finite chain
• Monoids of O-type, subword reversing, and ordered groups
• On semigroups of orientation-preserving partial permutations with restricted range