Let X n be a chain with n elements (n∈ ℕ), and let 𝒪𝒫 n be the monoid of all orientation-
preserving transformations of X n. In this article, for any nonempty subset Y of X n, we …

Abstract Let $ X_ {n}=\{1, 2,\ldots, n\} $ with its natural order and let ${\cal T} _ {n} $ be the full
transformation semigroup on $ X_ {n} $. A map $\alpha\in {\cal T} _ {n} $ is said to be order …

The rank of a finite semigroup is the smallest number of elements required to generate the
semigroup. A formula is given for the rank of an arbitrary (not necessarily regular) Rees …

In this paper we consider various classes of monoids of transformations of a finite chain,
including those of transformations that preserve or reverse either the order or the orientation …

The rank of a semigroup, an important and relevant concept in Semigroup Theory, is the
cardinality of a least-size generating set. Semigroups of transformations that preserve or …

Let Xn={1, 2,..., n}. On a partial transformation α: Dom α⊆ Xn→ Im α⊆ Xn of Xn the following
parameters are defined: the breadth or width of α is| Dom α|, the collapse of α is c (α)=|∪ t∈ …

Let 𝒪 𝒫 ℰ n be the monoid of all orientation-preserving and extensive full transformations on
{1, 2,…, n} ordered in the standard way. In this paper, we determine the minimum generating …

In this paper we consider the monoid $ DPC_n $ of all partial isometries of an $ n $-cycle
graph $ C_n $. We show that $ DPC_n $ is the submonoid of the monoid of all oriented …

The study of the semigroups OPn, of all orientation-preserving transformations on an n-
element chain, and ORn, of all orientation-preserving or orientationreversing transformations …

Abstract period.. In this note we consider various classes of monoids of transforma hyphen t
ions on a finite chain comma in particular of transformations that preserve or re hyphen …