New results from an algorithm for counting posets

In this paper we report on the success of a new technique for computing the number of unlabeled partial orders on n elements based on the partial order of partial orders ordered by containment. In addition to the number of partial orders, we obtain complete enumerations of the number of partial orders on n elements with r relations for n<-11, where r takes on all possible values. We point out some interesting sequences that arise in these tables.Supported by Natural Sciences and Engineering Research Council Grant No. OGP8053.