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

RootedEmbedding[g, v] constructs a rooted embedding of graph g with vertex v as the root. RootedEmbedding[g] constructs a rooted embedding with a center of g as the root.

ShowLabeledGraph[g] displays graph g according to its embedding, with each vertex labeled with its vertex number.ShowLabeledGraph[g, l] uses the i\[Null]^th element of list l ...

UnrankSetPartition[r, s, k] finds a k-block set partition of s with rank r. UnrankSetPartition[r, n, k] finds a k-block set partition of {1, 2, ..., n} with rank r.

UnrankSetPartition[r, set] finds a set partition of set with rank r. UnrankSetPartition[r, n] finds a set partition of {1, 2, ..., n} with rank r.

Vertices[g] gives the coordinates of each vertex of graph g embedded in a plane.Vertices[g, All] gives the embedding of the graph along with graphics options associated with ...

Decagon is a regular polygon with ten edges, for use with polytope functions.

Digon is a regular polygon with two edges, for use with polytope functions.

Dodecagon is a regular polygon with twelve edges, for use with polytope functions.

Heptagon is a regular polygon with seven edges, for use with polytope functions.