Maximal frequencies of equivalences with small classes

If e, E are equivalences on a finite set, then the frequency of e in E is the number of subequivalences of E which are isomorphic to e. Given an equivalence e on a certain set the problem arises of finding an equivalence E such that the frequency of e in E is maximal. In this paper we solve this problem for those equivalences e all of those classes have cardinality at most 2.