The paper gives explicit descriptions, cardinalities, ranks, and minimal generating sets for the group Γ_n and the monoids Σ_n and Δ_n defined by evenness conditions on restrictions to maximal proper subsets.
Fernandes, Oriented transformations on a finite chain: another description, Commun
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Groups of permutations that are even on maximal proper subsets, and related monoids
The paper gives explicit descriptions, cardinalities, ranks, and minimal generating sets for the group Γ_n and the monoids Σ_n and Δ_n defined by evenness conditions on restrictions to maximal proper subsets.