Before revision:  To resolve this issue, we give a formal proof of the correctness of a smart backtracking algorithm that computes the \delta-partitions of \alpha efficiently without a prior construction of the partitions of~\alpha. The algorithm does so by checking (ahead) two properties identifying parts of the search space that are devoid of any \delta-partition of~\alpha .
After revision:  To resolve this issue, we give a formal proof of the correctness of a smart backtracking algorithm that computes the \delta-partitions of \alpha in \Omega(nB_n) time where B_n is the Bell number .