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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.
- 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.
- Bilateral semidirect product decompositions of transformation monoidsPublication . Fernandes, Vítor H.; Quinteiro, TeresaIn this paper we consider the monoid OR(n) of all full transformations on a chain with n elements that preserve or reverse the orientation, as well as its submonoids OD(n) of all order-preserving or order-reversing elements, OP(n) of all orientation-preserving elements and O(n) of all order-preserving elements. By making use of some well known presentations, we show that each of these four monoids is a quotient of a bilateral semidirectproduct of two of its remarkable submonoids.