The monoid of ordered partitions of a natural number
type: Item
instance of: scholarly article
title: The monoid of ordered partitions of a natural number
zbMATH Open document ID: 0852.20050
DOI: 10.1007/BF02574119
author: T. G. Lavers
published in: Semigroup Forum
publication date: 1996-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/135468
review text: An operation is introduced making \(M\), the set of all sequences of nonnegative integers into a monoid shown to be isomorphic to the monoid of all partial, finite-to-one, order-preserving transformations \(f\) of the positive integers \(\mathbb{N}\), where \(\text{dom }f\) is an initial segment of \(\mathbb{N}\). A presentation is found for a submonoid \(S_n\) of \(M\) the elements of which are ordered partitions of a natural number \(n\), the posets of principal one-sided ideals of \(S_n\) are described, that for left ideals being the more complex: an algorithm is constructed for the Hasse diagram of the poset of left principal ideals of \(S_n\).
Mathematics Subject Classification ID: 20M20
Mathematics Subject Classification ID: 06A07
Mathematics Subject Classification ID: 20M12
Mathematics Subject Classification ID: 11P81
Mathematics Subject Classification ID: 20M05
Mathematics Subject Classification ID: 05A17
zbMATH DE Number: 895849
zbMATH Keywords: monoid of partial finite-to-one order-preserving transformations
zbMATH Keywords: sequences of nonnegative integers
zbMATH Keywords: positive integers
zbMATH Keywords: presentation
zbMATH Keywords: ordered partitions
zbMATH Keywords: posets of principal one-sided ideals
zbMATH Keywords: left ideals
zbMATH Keywords: algorithm
zbMATH Keywords: Hasse diagram
zbMATH Keywords: poset of left principal ideals
reviewed by: Peter M. Higgins
MaRDI profile type: Publication
cites work: Combinatorial results for semigroups of order-preserving mappings
cites work: DIVISORS OF SEMIGROUPS OF ORDER-PRESERVING MAPPINGS ON A FINITE CHAIN
cites work: Products of idempotents in certain semigroups of transformations
cites work: Q4126563
cites work: Q4872077
cites work: Enumerating nested and consecutive partitions
cites work: Q4325287
cites work: Catalan monoids, monoids of local endomorphisms, and their presentations
description: scientific article; zbMATH DE number 895849