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 …

Let T (X) be the full transformation monoid on a nonempty set X. An element f of T (X) is said
to be semi-balanced if the collapse of f is equal to the defect of f. In this paper, we prove that …

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 …

Full article: On the monoid of partial isometries of a finite star graph Skip to Main Content
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In this paper, we study partial automorphisms and, more generally, injective partial
endomorphisms of a finite undirected path from Semigroup Theory perspective. Our main …

Let X be a nonempty set, and let TX be the full transformation semigroup on X. For a partition
P={X i| i∈ I} of X, we consider the semigroup T (X, P)={f∈ TX|∀ X i∃ X j, X if⊆ X j}, the …

In this paper, we study the widely considered endomorphisms and weak endomorphisms of
a finite undirected path from monoid generators perspective. Our main aim is to determine …

Let X be a nonempty set and T _X TX the full transformation semigroup on X. For a partition
PP of X, we study semigroups T (X, P)={f ∈ T _X ∣ (∀ X_i ∈ P)(∃ X_j ∈ P)\; X_i f ⊆ X_j\} T …

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 …

Let P={Xi: i∈ I} be a partition of a set X. We say that a transformation f: X→ X preserves P if
for every Xi∈ P, there exists Xj∈ P such that Xif⊆ Xj. Consider the semigroup B (X, P) of all …