Presentations for some monoids of injective partial transformations on a finite chain.
type: Item
instance of: scholarly article
title: Presentations for some monoids of injective partial transformations on a finite chain.
zbMATH Open document ID: 1078.20060
author: Vítor H. Fernandes
author: Gracinda M. S. Gomes
author: Manuel M. Jesus
published in: Southeast Asian Bulletin of Mathematics
publication date: 2005-03-21T00:00:00Z
review text: 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.
reviewed by: Peter M. Higgins
Mathematics Subject Classification ID: 20M20
Mathematics Subject Classification ID: 20M05
zbMATH DE Number: 2148381
zbMATH Keywords: monoids of transformations
zbMATH Keywords: order-preserving transformations
zbMATH Keywords: orientation-preserving transformations
zbMATH Keywords: presentations
zbMATH Keywords: numbers of relations
describes a project that uses: GAP
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 2148381