Combinatorial results for semigroups of order-preserving partial transformations.
type: Item
instance of: scholarly article
title: Combinatorial results for semigroups of order-preserving partial transformations.
zbMATH Open document ID: 1057.20046
published in: Journal of Algebra
publication date: 2004-09-23T00:00:00Z
review text: This paper gathers together some combinatorial results for the semigroup \(S=\mathcal{PO}_n\), the semigroup of all partial order-preserving mappings on a finite \(n\)-chain. Counting the numbers of mappings with domains and ranges of particular cardinalities eventually leads to a second-order nonlinear recurrence for \(|S|\). A similar set of results is obtained for \(e_n\), the number of idempotents. On this occasion the solution is explicitly determined in terms of powers of the golden ratio and curiously it transpires that \(e_n-1\) is a multiple of five. The final section proves counting results on the sizes of classes determined by Green's relations on \(S\).
Mathematics Subject Classification ID: 20M20
Mathematics Subject Classification ID: 05A15
zbMATH DE Number: 2102503
zbMATH Keywords: partial order-preserving mappings
zbMATH Keywords: golden ratio
zbMATH Keywords: idempotents
zbMATH Keywords: semigroups of transformations
author: Abdallah Laradji
author: A. Umar
reviewed by: Peter M. Higgins
describes a project that uses: OEIS
MaRDI profile type: Publication
full work available at URL: j.jalgebra.2003.10.023
OpenAlex ID: W2053476865
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DOI: 10.1016/J.JALGEBRA.2003.10.023
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description: scientific article; zbMATH DE number 2102503