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- Presentations for monoids of finite partial isometriesPublication . Quinteiro, Teresa; Fernandes, Vítor H.In this paper we give presentations for the monoid DPn of all partial isometries on {1,..., n} and for its submonoid ODPn of all order-preserving partial isometries.
- On semigroups of endomorphisms of a chain with restricted rangePublication . Fernandes, Vitor H.; Honyam, Preeyanuch; Quinteiro, Teresa; Singha, BoorapaLet X be a finite or infinite chain and let be the monoid of all endomorphisms of X. In this paper, we describe the largest regular subsemigroup of and Green's relations on. In fact, more generally, if Y is a nonempty subset of X and is the subsemigroup of of all elements with range contained in Y, we characterize the largest regular subsemigroup of and Green's relations on. Moreover for finite chains, we determine when two semigroups of the type are isomorphic and calculate their ranks.
- On Semigroups of Orientation-preserving Transformations with Restricted RangePublication . Fernandes, Vitor H.; Honyam, Preeyanuch; Quinteiro, Teresa; Singha, BoorapaLet Xn be a chain with n elements (n ∈ ℕ), and let 𝒪𝒫n be the monoid of all orientation-preserving transformations of Xn. In this article, for any nonempty subset Y of Xn, we consider the subsemigroup 𝒪𝒫n(Y) of 𝒪𝒫n of all transformations with range contained in Y: We describe the largest regular subsemigroup of 𝒪𝒫n(Y), which actually coincides with its subset of all regular elements. Also, we determine when two semigroups of the type 𝒪𝒫n(Y) are isomorphic and calculate their ranks. Moreover, a parallel study is presented for the correspondent subsemigroups of the monoid 𝒪ℛn of all either orientation-preserving or orientation-reversing transformations of Xn.
- Ranks and presentations of some normally ordered inverse semigroupsPublication . Caneco, Rita; Fernandes, Vítor Hugo; Quinteiro, TeresaIn this paper we compute the rank and exhibit a presentation for the monoids of all P-stable and P-order preserving partial permutations on a finite set Omega, with P an ordered uniform partition of Omega. These (inverse) semigroups constitute a natural class of generators of the pseudovariety of inverse semigroups N O of all normally ordered (finite) inverse semigroups.
- A note on bilateral semidirect product decompositions of some monoids of order-preserving partial permutationsPublication . Fernandes, Vítor Hugo; Quinteiro, TeresaIn this note we consider the monoid PODIn of all monotone partial permutations on {1,....,n} and its submonoids DPn, POIn and ODPn of all partial isometries, of all order-preserving partial permutations and of all order-preserving partial isometries, respectively. We prove that both the monoids POIn and ODPn are quotients of bilateral semidirect products of two of their remarkable submonoids, namely of extensive and of co-extensive transformations. Moreover, we show that PODIn is a quotient of a semidirect product of POIn and the group C-2 of order two and, analogously, DPn is a quotient of a semidirect product of ODPn and C-2.
- The cardinal of various monoids of transformations that preserve a uniform partitionPublication . Fernandes, Vítor H.; Quinteiro, TeresaIn this paper we give formulas for the number of elements of the monoids ORm x n of all full transformations on it finite chain with tun elements that preserve it uniform m-partition and preserve or reverse the orientation and for its submonoids ODm x n of all order-preserving or order-reversing elements, OPm x n of all orientation-preserving elements, O-m x n of all order-preserving elements, O-m x n(+) of all extensive order-preserving elements and O-m x n(-) of all co-extensive order-preserving elements.