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

OctahedralGraph returns the graph corresponding to the octahedron, a Platonic solid.

Optimum is a value that the option Algorithm can take on when used in functions VertexColoring and VertexCover.

Ordered is an option to the functions KSubsetGroup and KSubsetGroupIndex that tells the functions whether they should treat the input as sets or tuples.

Parent is a tag used as an argument to the function AllPairsShortestPath in order to inform this function that information about parents in the shortest paths is also wanted.

PermutationQ[p] yields True if p is a list representing a permutation and False otherwise.

Permute[l, p] permutes list l according to permutation p.

RandomHeap[n] constructs a random heap on n elements.

RandomVertices[g] assigns a random embedding to graph g.

Runs[p] partitions p into contiguous increasing subsequences.