arXiv subjects
Publications and source records attributed to Vítor Hugo Fernandes.
In this paper, we consider the inverse submonoids $AM_n$ of monotone transformations and $AO_n$ of order-preserving transformations of the alternating inverse monoid $AI_n$ on a chain with $n$ elements. We compute the cardinalities, describe the Green's structures and the congruences, and calculate the ranks of these two submonoids of $AI_n$.
In this paper, we consider the inverse submonoids $AOR_n$ of oriented transformations and $AOP_n$ of orientation-preserving transformations of the alternating inverse monoid $AI_n$ on a chain with $n$ elements. We compute the cardinalities, describe the Green's structures and the congruences, and calculate the ranks of $AOR_n$ and $AOP_n$.
In this paper we consider the monoid $DPS_n$ of all partial isometries of a star graph $S_n$ with $n$ vertices. Our main objectives are to determine the rank and to exhibit a presentation of $DPS_n$. We also describe Green's relations of $DPS_n$ and calculate its cardinal.
In this paper we consider endomorphisms of a finite directed path from monoid generators perspective. Our main aim is to determine the rank of the monoid $\wEnd\vec{P}_n$ of all weak endomorphisms of a directed path with $n$ vertices, which is a submonoid of the widely studied monoid $\On$ of all order-preserving transformations of a $n$-chain. Also, we describe the regular elements of $\wEnd\vec{P}_n$ and calculate its size and number of idempotents.