Presentations for Some Monoids of Injective Partial Transformations on a Finite Chain.

In this paper we consider three natural extensions of the inverse monoid POIn of all order preserving injective partial transformations of a chain with n elements. Namely, the inverse monoid PODIn consisting of all injective partial transformations on a chain with n elements which are either order preserving or order reversing, the inverse monoid POPIn of all orientation preserving injective partial transformations on a chain with n elements and the inverse monoid PORIn whose elements are all orientation preserving together with all orientation reversing injective partial transformations on a chain with n elements. Our main aim is to exhibit a presentation for POPIn in terms of n generators and ½(n² + 7n - 2) relations, a presentation for POPIn in terms of 2 generators and 2n relations and, finally, a presentation for PORIn in terms of 3 generators and 2n + 4 relations. [ABSTRACT FROM AUTHOR]