Presentations for some monoids of injective partial transformations on a finite chain.
The paper seeks small, perhaps minimal presentations of certain monoids of injective partial transformations on a finite chain. The monoid of all injective partial mappings on an \(n\)-chain which are either order-preserving or order-reversing is presented by \(n\) generators and \(\tfrac 12(n^2+7n-2)\) relations; the monoid of all orientation preserving injective partial mappings is two-generated on \(2n\) relations; the monoid of all partial one-to-one orientation preserving or reversing mappings is three-generated with \(2n+4\) relations. Although computational tools were used in the search for these presentations, the paper is largely self-contained, although not all details are recorded.
scientific article; zbMATH DE number 2148381