On the Computation of Isolated Sublattices

Kurzfassung

In this short notice we give some ideas how to compute isolated sublattices which can be used to derive a recursive algorithm for the computation of the number of closure operators on a finite lattice. We give an asymptoticaly optimal algorithm for deciding the existence and - in the case of existence - the computation of useful nontrivial isolated summit sublattices. The general case (i.e., an optimal algorithm for the computation of general nontrivial useful isolated sublattices) remains unsolved, however, we try to give some ideas and hints for future research.