Publications

Export 60 results:
Sort by: [ Author  (Asc)] Title Type Year
A B C D E F G H I J K L M N O P Q R S T U V W X Y Z 
A
André, J. M., V. H. Fernandes, and J. D. Mitchell. "Largest 2-generated subsemigroups of the symmetric inverse semigroup." Proc. Edinb. Math. Soc. (2). 50 (2007): 551-561.Website
Araújo, João, Vítor H. Fernandes, Manuel M. Jesus, Victor Maltcev, and James D. Mitchell. "Automorphisms of partial endomorphism semigroups." Publicationes Mathematicae Debrecen. 79.1-2 (2011): 23-39.
Araújo, Isabel M., Mário J. J. Branco, Vitor H. Fernandes, Gracinda M. S. Gomes, and N. Ruškuc. "On generators and relations for unions of semigroups." Semigroup Forum. 63 (2001): 49-62.
C
Caneco, Rita, Vítor H. Fernandes, and Teresa M. Quinteiro. "Ranks and presentations of some normally ordered inverse semigroups." Periodica Mathematica Hungarica (DOI 10.1007/s10998-022-00448-8). 85 (2022): 435-447. AbstractWebsite

In 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 ${\sf NO}$ of all normally ordered (finite) inverse
semigroups.

Cicalò, Serena, Vítor H. Fernandes, and Csaba Schneider. "Partial transformation monoids preserving a uniform partition." Semigroup Forum (DOI 10.1007/s00233-014-9629-5). 90.2 (2015): 532-544. AbstractWebsite

The objective of this paper is to study the monoid of all partial
transformations of a finite set that preserve a uniform partition. In addition
to proving that this monoid is a quotient of a wreath product with respect to a
congruence relation, we show that it is generated by 5 generators, we compute
its order and determine a presentation on a minimal generating set.

Cordeiro, E., M. Delgado, and V. H. Fernandes. "Relative abelian kernels of some classes of transformation monoids." Bull. Austral. Math. Soc.. 73 (2006): 375-404.Website
D
Delgado, Manuel, and Vítor H. Fernandes. "Rees quotients of numerical semigroups." Portugaliae Mathematica. 70.2 (2013): 93-112. AbstractWebsite

We introduce a class of finite semigroups obtained by considering Rees
quotients of numerical semigroups.
Several natural questions concerning this class, as well as particular
subclasses obtained by considering some special ideals, are answered while
others remain open. We exhibit nice presentations for these semigroups and
prove that the Rees quotients by ideals of N, the positive integers under
addition, constitute a set of generators for the pseudovariety of commutative
and nilpotent semigroups.

Delgado, Manuel, and Vítor H. Fernandes. "Solvable monoids with commuting idempotents." Int. J. Algebra Comput.. 15 (2005): 547-570. Abstract

The notion of the Abelian kernel of a finite monoid is a generalization of that of the derived subgroup of a finite group. A monoid $M$ is then called solvable if its chain of Abelian kernels terminates with the submonoid of $M$ generated by its idempotents. The main result of this paper is that the finite idempotent commuting monoids bearing this property are precisely those whose subgroups are solvable. In particular any finite aperiodic monoid is Abelian-solvable in this sense. A generalization of the main result of this paper has been published [in Int. J. Algebra Comput. 14, No. 5-6, 655-665 (2004; Zbl 1081.20067)] by the authors and ıt S. Margolis and ıt B. Steinberg.

Delgado, Manuel, V{\'ı}tor H. Fernandes, Stuart Margolis, and Benjamin Steinberg. "On semigroups whose idempotent-generated subsemigroup is aperiodic." Internat. J. Algebra Comput.. 14 (2004): 655-665.Website
Delgado, Manuel, and Vítor H. Fernandes. "Abelian kernels of some monoids of injective partial transformations and an application." Semigroup Forum. 61 (2000): 435-452.Website
Delgado, Manuel, and Vítor H. Fernandes. "Abelian kernels of monoids of order-preserving maps and of some of its extensions." Semigroup Forum. 68 (2004): 335-356.Website
Delgado, Manuel, and Vítor H. Fernandes. "Abelian kernels, solvable monoids and the abelian kernel length of a finite monoid." Semigroups and languages. World Sci. Publ., River Edge, NJ, 2004. 68-85.
Dimitrova, I., Vítor H. Fernandes, and J. Koppitz. "On partial endomorphisms of a star graph." (Submitted). AbstractWebsite

In this paper we consider the monoids of all partial endomorphisms, of all partial weak endomorphisms, of all injective partial endomorphisms, of all partial strong endomorphisms and of all partial strong weak endomorphisms of a star graph with a finite number of vertices. Our main objective is to determine their ranks. We also describe their Green's relations, calculate their cardinalities and study their regularity.

Dimitrova, I., Vítor H. Fernandes, J. Koppitz, and T. M. Quinteiro. "Ranks of monoids of endomorphisms of a finite undirected path (DOI: 10.1007/s40840-019-00762-4)." Bulletin of the Malaysian Mathematical Sciences Society. 43 (2020): 1623-1645. AbstractWebsite

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 the ranks of the monoids $wEnd P_n$ and $End P_n$ of all weak endomorphisms and all endomorphisms of the undirected path $P_n$ with $n$ vertices. We also consider strong and strong weak endomorphisms of $P_n$.

Dimitrova, I., Vítor H. Fernandes, J. Koppitz, and T. M. Quinteiro. "On monoids of endomorphisms of a cycle graph." Mathematica Slovaca (In Press). Abstract

In this paper we consider endomorphisms of an undirected cycle graph from Semigroup Theory perspective. Our main aim is to present a process to determine sets of generators with minimal cardinality for the monoids $wEnd(C_n)$ and $End(C_n)$ of all weak endomorphisms and all endomorphisms of an undirected cycle graph $C_n$ with $n$ vertices. We also describe Green's relations and regularity of these monoids and calculate their cardinalities.

Dimitrova, I., Vítor H. Fernandes, J. Koppitz, and T. M. Quinteiro. "On three submonoids of the dihedral inverse monoid on a finite set." Bulletin of the Malaysian Mathematical Sciences Society (DOI 10.1007/s40840-023-01620-0; Online 11 Dec 2023). 47 (2024): 27. AbstractWebsite

In this paper we consider three submonoids of the dihedral inverse monoid DI_n, namely its submonoids OPDI_n, MDI_n and ODI_n of all orientation-preserving, monotone and order-preserving transformations, respectively. For each of these three monoids, we compute the cardinal, give descriptions of Green's relations and determine the rank.

Dimitrova, I., Vítor H. Fernandes, and J. Koppitz. "The maximal subsemigroups of semigroups of transformations preserving or reversing the orientation on a finite chain." Publicationes Mathematicae Debrecen. 81.1-2 (2012): 11-29.
Dimitrova, I., Vítor H. Fernandes, J. Koppitz, and T. M. Quinteiro. "Presentations for three remarkable submonoids of the dihedral inverse monoid on a finite set." Semigroup Forum (DOI 10.1007/s00233-023-10396-5; Online 31 Oct 2023). 107 (2023): 315-338. AbstractWebsite

In this paper we consider the submonoids OPDI_n, MDI_n and ODI_n of the dihedral inverse monoid DI_n of all orientation-preserving, monotone and order-preserving transformations, respectively. Our goal is to exhibit presentations for each of these three monoids.

Dimitrova, I., Vítor H. Fernandes, and J. Koppitz. "A note on generators of the endomorphism semigroup of an infinite countable chain." Journal of Algebra and its Applications (DOI: 10.1142/S0219498817500311). 16 (2017): 1750031 (9 pages). AbstractWebsite

In this note, we consider the semigroup $O(X)$ of all order endomorphisms of an infinite chain $X$ and the subset $J$ of $O(X)$ of all transformations $\alpha$ such that $|Im(\alpha)|=|X|$. For an infinite countable chain $X$, we give a necessary and sufficient condition on $X$ for $O(X) = < J >$ to hold. We also present a sufficient condition on $X$ for $O(X) = < J >$ to hold, for an arbitrary infinite chain $X$.

Dimitrova, I., Vítor H. Fernandes, J. Koppitz, and T. M. Quinteiro. "Partial Automorphisms and Injective Partial Endomorphisms of a Finite Undirected Path." Semigroup Forum. 103 (2021): 87-105. AbstractWebsite

In 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 the monoids IEnd(P_n) and PAut(P_n) of all injective partial endomorphisms and of all partial automorphisms of the undirected path P_n with n vertices. We also describe Green's relations of PAut(P_n) and IEnd(P_n) and calculate their cardinals.

F
Fernandes, Vítor H., Gracinda M. S. Gomes, and Manuel M. Jesus. "Presentations for some monoids of injective partial transformations on a finite chain." Southeast Asian Bull. Math.. 28 (2004): 903-918.
Fernandes, Vítor H. "On the monoid of partial isometries of a wheel graph." Asian-European Journal of Mathematics (DOI 10.1142/S1793557123502388; Online 16 Dec 2023). 17.1 (2024): 2350238 (18 pages). AbstractWebsite

In this paper, we consider the monoid DPW_n of all partial isometries of a wheel graph W_n with n+1 vertices. Our main objective is to determine the rank of DPW_n. In the process, we also compute the ranks of three notable subsemigroups of DPW_n. We also describe Green's relations of DPW_n and of its three considered subsemigroups.

Fernandes, Vítor H., Gracinda M. S. Gomes, and Manuel M. Jesus. "Congruences on monoids of order-preserving or order-reversing transformations on a finite chain." Glasg. Math. J.. 47 (2005): 413-424.Website
Fernandes, Vítor H., and Teresa M. Quinteiro. "Bilateral semidirect product decompositions of transformation monoids." Semigroup Forum. 82 (2011): 271-287. Abstract
Summary: In this paper we consider the monoid $\mathcal {OR}_{n}$ of all full transformations on a chain with $n$ elements that preserve or reverse the orientation, as well as its submonoids $\mathcal {OD}_{n}$ of all order-preserving or order-reversing elements, $\mathcal {OP}_{n}$ of all orientation-preserving elements and $\mathcal {O}_{n}$ 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 semidirect product of two of its remarkable submonoids.
Fernandes, Vítor H., J. Koppitz, and T. Musunthia. "The rank of the semigroup of all order-preserving transformations on a finite fence." Bulletin of the Malaysian Mathematical Sciences Society (DOI: 10.1007/s40840-017-0598-1). 42.5 (2019): 2191-2211. AbstractWebsite

A zig-zag (or fence) order is a special partial order on a (finite) set. In this paper, we consider the semigroup $TF_{n}$ of all
order-preserving transformations on an $n$-element zig-zag ordered set. We determine the rank of $TF_{n}$ and provide a minimal generating set for $TF_{n}$. Moreover, a formula for the number of idempotents in $TF_{n}$ is given.