Majors of functions
type: Item
instance of: scholarly article
title: Majors of functions
zbMATH Open document ID: 1412.08002
author: Miguel Couceiro
author: Erkko Lehtonen
published in: Order
publication date: 2018-07-27T00:00:00Z
full work available at URL: Majors-HAL.pdf
review text: A function \(f\) from the \(n\)-th power of \(A\) to \(B\) is called a minor of another function \(g\) from the \(m\)-th power of \(A\) to \(B\), or \(g\) is a major of \(f\), if \(f\) can be obtained from \(g\) by identification of arguments, permutation of arguments, or introduction or deletion of inessential arguments. The minor relation constitutes a quasi-order on the set of functions of several arguments from \(A\) to \(B\). The authors investigate upper covers and common upper bounds of pairs of functions. They show that two functions of arities \(m\) and \(n\) have a common lower bound if and only if they have a common upper bound, and if a common upper bound exists, then there is one of arity \(m+n-1\). The possible essential arities of upper covers of functions are also determined.
Mathematics Subject Classification ID: 08A40
Mathematics Subject Classification ID: 06A06
Mathematics Subject Classification ID: 06A07
Mathematics Subject Classification ID: 06E30
zbMATH DE Number: 6911224
zbMATH Keywords: function of several arguments
zbMATH Keywords: Boolean function
zbMATH Keywords: essential arity
zbMATH Keywords: minor order
zbMATH Keywords: upper cover
reviewed by: Anna Romanowska
MaRDI profile type: Publication
OpenAlex ID: W2616638360
cites work: On the Number of Operations in a Clone
cites work: Join-irreducible Boolean functions
cites work: Generalizations of Świerczkowski's lemma and the arity gap of finite functions
cites work: Parametrized arity gap
cites work: On a quasi-ordering on Boolean functions
cites work: Partial orders induced by quasilinear clones
cites work: Essential arities of term operations in finite algebras
DOI: 10.1007/S11083-017-9428-1
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description: scientific article; zbMATH DE number 6911224