Collapsing monoids consisting of permutations and constants
type: Item
instance of: scholarly article
title: Collapsing monoids consisting of permutations and constants
zbMATH Open document ID: 1156.08003
author: Miklós Dormán
published in: Algebra Universalis
publication date: 2009-01-29T00:00:00Z
review text: Let \(A\) be a finite set with \(| A| >1\), \(M\) a transformation monoid over \(A\) consisting of \(c\) constant functions and some permutations, and let \(i(M)\) denote the number of all clones over \(A\) having \(M\) as its set of unary members. For \(c\geq1\), all \(M\) with \(i(M)=1\) are determined. Moreover, it is shown that \(i(M)\) is infinite in case \(c=1\) and that there exist infinitely many \(M\) with \(c\geq3\) and \(i(M)=2\).
reviewed by: Helmut Länger
Mathematics Subject Classification ID: 08A40
zbMATH DE Number: 5500446
zbMATH Keywords: clone
zbMATH Keywords: unary part
zbMATH Keywords: transformation monoid
zbMATH Keywords: monoidal interval
zbMATH Keywords: collapsing
zbMATH Keywords: constant function
zbMATH Keywords: permutation
MaRDI profile type: Publication
full work available at URL: s00012-008-2095-8
OpenAlex ID: W2070481021
DOI: 10.1007/S00012-008-2095-8
description: scientific article; zbMATH DE number 5500446