We say that an automorphismΦ\PhiofE∗{\mathcal {E}^ \ast }(the lattice of recursively enumerable sets modulo the finite sets) isinducedby a permutationpiff for alle,Φ(We)=∗p(We)\Phi ({W_e}){ = ^ \ast }p({W_e}). A permutationhis called apresentationofΦ\Phiiff for alle,Φ(We)=∗Wh(e)\Phi ({W_e}){ = ^\ast }{W_{h(e)}}. In this paper, we will explore the degree-theoretic connections between these two notions. Using a new proof of the well-known fact that every automorphism is induced by a permutationp, we show that such apcan be found recursively inh⊕∅h \oplus \emptyset, wherehis a presentation ofΦ\Phi. The main result of the paper is to show that there is an effective automorphism ofE∗{\mathcal {E}^ \ast }which is not induced by aΔ2{\Delta _2}-permutation.