Eliminating recursion from combinatoric procedures

The problem of eliminating linear and binary recursion has received quite a deal of attention. Less has been given to the elimination of the more general form of recursion that arises in combinatorics. In this paper we extend earlier work and produce two pairs of equivalent schemata. The correspondences between these schemata and the classical combinatoral problems are given and two applied examples: topological sorting and the set covering problem, are discussed in detail.