Ranks and presentations of some normally ordered inverse semigroups

Citation:
Caneco, Rita, Vítor H. Fernandes, and Teresa M. Quinteiro. "Ranks and presentations of some normally ordered inverse semigroups." (Submitted).

Abstract:

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.

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