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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.