Generating Sets of Finite Transformation Semigroups K n r and PK n r

İngilizce (OpenAlex)

Let P n and T n be the partial transformation and the full transformation semigroups on the set {1,…, n}, respectively. In this paper we find necessary and sufficient conditions for any set of partial transformations of height r in the subsemigroup PK(n, r) = {α ∈P n : |im (α)| ≤r} of P n to be a (minimal) generating set of PK(n, r); and similarly, for any set of full transformations of height r in the subsemigroup K(n, r) = {α ∈T n : |im (α)| ≤r} of T n to be a (minimal) generating set of K(n, r) for 2 ≤ r ≤ n − 1.