NextLexicographicSubset[l, s] gives the lexicographic successor of subset s of set l.

NumberOfCompositions[n, k] counts the number of distinct compositions of integer n into k parts.

NumberOfPartitions[n] counts the number of integer partitions of n.

NumberOfPermutationsByCycles[n, m] gives the number of permutations of length n with exactly m cycles.

NumberOfPermutationsByTypes[l] gives the number of permutations of type l.

NumberOfSpanningTrees[g] gives the number of labeled spanning trees of graph g.

RankRGF[f] returns the rank of a restricted growth function (RGF) f in the lexicographic order of all RGFs.

RankSubset[l, s] gives the rank, in canonical order, of subset s of set l.

StronglyConnectedComponents[g] gives the strongly connected components of directed graph g as lists of vertices.

V[g] gives the order or number of vertices of the graph g.