Abstract Let [n]={1, 2,…, n} be a finite chain and let P n be the semigroup of partial
transformations on [n]. Let CP n={α∈ P n:(for all x, y∈ Dom α)| x α− y α|≤| x− y|} be the …

The main subject of this paper is the description of the congruences on certain monoids of
transformations on a finite chain Xn with n elements. Namely, we consider the monoids ORn …

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 …

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∈ …

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 …

This paper presents a unified framework for determining the congruences on a number of
monoids and categories of transformations, diagrams, matrices and braids, and on all their …

In this paper we give formulas for the number of elements of the monoids ORm× n of all full
transformations on a finite chain with mn elements that preserve a uniform m-partition and …

Mal'′ cev described the congruences of the monoid T _n T n of all full transformations on a
finite set X_n={1,\dots, n\} X n= 1,⋯, n. Since then, congruences have been characterized in …