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- Ranks of monoids of endomorphisms of a finite undirected pathPublication . Dimitrova, Ilinka; Fernandes, Vítor Hugo; Koppitz, J.; Quinteiro, TeresaIn 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 the ranks of the monoids wEndPn and EndPn of all weak endomorphisms and all endomorphisms of the undirected path Pn with n vertices. We also consider strong and strong weak endomorphisms of Pn.
- 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.
- Partial automorphisms and injective partial endomorphisms of a finite undirected pathPublication . Dimitrova, Ilinka; Fernandes, V. H.; Koppitz, J.; Quinteiro, TeresaIn this paper, we study partial automorphisms and, more generally, injective partial endomorphisms of a finite undirected path from Semigroup Theory perspective. Our main objective is to give formulas for the ranks of themonoids IEnd(P-n) and PAut(P-n) of all injective partial endomorphisms and of all partial automorphisms of the undirected path Pn with n vertices. We also describe Green's relations of PAut(P-n) and IEnd(P-n) and calculate their cardinals.