Presentations for two extensions of the monoid of order-preserving mappings on a finite chain (Q1586826)

The article gives a new presentation for the monoid of orientation-preserving mappings on the set \(\{1,\ldots,n\}\) having two generators and \(n+2\) relations. Applying this result to orientation-preserving or reversing mappings on this set the authors obtain a presentation having three generators and \(n+6\) relations.