Majors of functions
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.
scientific article; zbMATH DE number 6911224
scientific article