Let \(X\) be a set and \((T_X,\circ)\) the full transformation semigroup on \(X\). If \(X\) is finite, then \(T_X=E\circ S_X=S_X\circ E\), where \(E\) denotes the set of all idempotents in \(T_X\) and \(S_X\) the group of all permutations on \(X\) [see J. Fountain and A. Lewin, Math. Proc. Camb. Philos. Soc. 114, No. 2, 303-319 (1993; Zbl 0819.20070)]. In the paper under review it is shown that if \(X\) is infinite, \(E\circ S_X=S_X\circ E=B\), the set of all semibalanced elements of \(T_X\). The question is answered which set \(M\) of elements in \(T_X\) has to be added in order that \(E\cup S_X\cup M\) generates \(T_X\). It is proved that precisely two transformations are sufficient. An analogous investigation is performed with respect to \(PT_X\), the semigroup of all partial mappings of \(X\), and an analogous answer is obtained.