Collapsing monoids consisting of permutations and constants
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 \(i(M)=2\).
scientific article; zbMATH DE number 5500446