NumberOfKPaths[g, v, k] returns a sorted list that contains the number of paths of length k to different vertices of g from v.NumberOfKPaths[al, v, k] behaves identically, ...

NumberOfNecklaces[n, nc, Cyclic] returns the number of distinct ways in which an n-bead necklace can be colored with nc colors, assuming that two colorings are equivalent if ...

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.

NumberOfPermutationsByInversions[n, k] gives the number of permutations of length n with exactly k inversions. NumberOfPermutationsByInversions[n] gives a table of the number ...

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

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

NumberOfTableaux[p] uses the hook length formula to count the number of Young tableaux with shape defined by partition p.

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

OddGraph[n] returns the graph whose vertices are the size-(n - 1) subsets of a size-(2 nTraditionalForm\`\[Dash]1) set and whose edges connect pairs of vertices that ...