Notes on shuffle/exchange type permutation sets

Properties of some shuffle/exchange type permutation sets are studied from operational points of view. The permutation sets studied are Ω, Ω^-1, Ψ, L, and U; Ω and Ω^-1 are, respectively, the omega and inverse omega permutation sets, Ω≡(Ω∩Ω^-1); and L and U are, respectively, the admissible lower and upper triangular permutation sets. Several intuitive operations are introduced. Based on these operations, important known results relating to these sets are readdressed. The recursive nature of the sets is also discussed